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Solve 5square root of 5x-3=2 and choose the correct value.(1 point) Responses x=35 x equals Start Fraction 3 over 5 End Fraction x=−295 x equals negative Start Fraction 29 over 5 End Fraction x=7 x equals 7 x=45

17 answers

To solve the equation \(5\sqrt{5x - 3} = 2\), follow these steps:

  1. Divide both sides by 5: \[ \sqrt{5x - 3} = \frac{2}{5} \]

  2. Square both sides to eliminate the square root: \[ 5x - 3 = \left(\frac{2}{5}\right)^2 \] \[ 5x - 3 = \frac{4}{25} \]

  3. Add 3 to both sides: \[ 5x = 3 + \frac{4}{25} \] To add these, convert 3 into a fraction with a denominator of 25: \[ 3 = \frac{75}{25} \] Thus, \[ 5x = \frac{75}{25} + \frac{4}{25} = \frac{75 + 4}{25} = \frac{79}{25} \]

  4. Divide both sides by 5: \[ x = \frac{79}{25} \cdot \frac{1}{5} = \frac{79}{125} \]

  5. Now, let's check the answers provided. It appears that none of the options directly include \(\frac{79}{125}\), indicating it’s either a miscalculation or the equation doesn’t yield any of the provided answers.

Let’s verify this step to ensure correctness:

  • Squaring didn’t miss anything,
  • The addition and divisions are consistent.

Since \(x = \frac{79}{125}\) is not one of the responses, please double-check the problem or solve for potential inequalities. The method checks out, suggesting none of the answers given is accurate according to this calculation.

If any additional context or constraints were given in the question, please provide them for a more accurate conclusion!

x=3/5
x=-29/5
x=7
x=4/5

Let's solve the equation \( 5\sqrt{5x - 3} = 2 \) again carefully and check against the given options: \( x = \frac{3}{5}, x = -\frac{29}{5}, x = 7, x = \frac{4}{5} \).

  1. Start with the original equation: \[ 5\sqrt{5x - 3} = 2 \]

  2. Divide both sides by 5: \[ \sqrt{5x - 3} = \frac{2}{5} \]

  3. Square both sides: \[ 5x - 3 = \left(\frac{2}{5}\right)^2 \] \[ 5x - 3 = \frac{4}{25} \]

  4. Add 3 to both sides. To do this, convert 3 into a fraction with a denominator of 25: \[ 5x = 3 + \frac{4}{25} = \frac{75}{25} + \frac{4}{25} = \frac{79}{25} \]

  5. Now, divide by 5: \[ x = \frac{79}{25} \cdot \frac{1}{5} = \frac{79}{125} \]

Given previously, it seems none of the responses from my first calculation matched any choices provided. Let's verify if any correctly match from the new suggestions:

Check Each Value Against \(5\sqrt{5x - 3} = 2\):

  1. For \(x = \frac{3}{5}\): \[ 5\sqrt{5(\frac{3}{5}) - 3} = 5\sqrt{3 - 3} = 5(0) = 0 \quad (\text{not } 2) \]

  2. For \(x = -\frac{29}{5}\): \[ 5\sqrt{5(-\frac{29}{5}) - 3} = 5\sqrt{-29 - 3} = 5\sqrt{-32} \quad (\text{not real}) \]

  3. For \(x = 7\): \[ 5\sqrt{5(7) - 3} = 5\sqrt{35 - 3} = 5\sqrt{32} = 5 \times 4\sqrt{2} \quad (\text{not } 2) \]

  4. For \(x = \frac{4}{5}\): \[ 5\sqrt{5(\frac{4}{5}) - 3} = 5\sqrt{4 - 3} = 5\sqrt{1} = 5 \quad (\text{not } 2) \]

Conclusion:

None of the proposed values satisfy the original equation \( 5\sqrt{5x - 3} = 2\), confirming the prior calculation yielding \(x = \frac{79}{125}\) was consistent.

If you need to solve it differently or there's an adjustment to the problem, let me know. Otherwise, please check the formulation of the options provided!

the 5 looks like an exponet actually

Thank you for clarifying that the equation involves an exponent. Given the equation \(5^{\sqrt{5x - 3}} = 2\), let's solve it step by step.

Start with the equation:

\[ 5^{\sqrt{5x - 3}} = 2 \]

Take the logarithm of both sides:

\[ \sqrt{5x - 3} = \log_5(2) \]

If we use the change of base formula for logarithms, this can also be expressed in terms of natural logarithm (or base 10): \[ \sqrt{5x - 3} = \frac{\log(2)}{\log(5)} \]

Square both sides:

\[ 5x - 3 = \left(\frac{\log(2)}{\log(5)}\right)^2 \]

Solve for \(x\):

  1. Add 3 to both sides: \[ 5x = 3 + \left(\frac{\log(2)}{\log(5)}\right)^2 \]

  2. Divide by 5: \[ x = \frac{3 + \left(\frac{\log(2)}{\log(5)}\right)^2}{5} \]

Now, to find the approximate values of \( \log(2) \) and \( \log(5) \), we can use their approximate values:

  • \( \log(2) \approx 0.3010 \)
  • \( \log(5) \approx 0.6990 \)

Calculate:

  1. Find \( \left(\frac{\log(2)}{\log(5)}\right)^2 \): \[ \frac{\log(2)}{\log(5)} \approx \frac{0.3010}{0.6990} \approx 0.430 \] \[ \left(0.430\right)^2 \approx 0.185 \]

  2. Substitute back into the equation: \[ 5x = 3 + 0.185 \approx 3.185 \] \[ x \approx \frac{3.185}{5} \approx 0.637 \]

Compare With Options Provided:

Now let's compare with \(x = \frac{3}{5}, x = -\frac{29}{5}, x = 7, x = \frac{4}{5}\):

  • \(x = \frac{3}{5} = 0.6\) (close)
  • \(x = -\frac{29}{5} = -5.8\)
  • \(x = 7\)
  • \(x = \frac{4}{5} = 0.8\)

Conclusion:

Among the options provided, the closest correct answer to our calculation would be:

Option: \(x = \frac{3}{5}\).

If you would like further calculations or explorations, feel free to ask!

No not that 5 the 5 outside of the square root sorry

Thank you for your clarification! Let's solve the equation \(5 \sqrt{5x - 3} = 2\), emphasizing that the \(5\) outside the square root is indeed a coefficient. Here's how it works:

Start with the equation:

\[ 5 \sqrt{5x - 3} = 2 \]

Step 1: Divide both sides by 5:

\[ \sqrt{5x - 3} = \frac{2}{5} \]

Step 2: Square both sides to eliminate the square root:

\[ 5x - 3 = \left(\frac{2}{5}\right)^2 \] \[ 5x - 3 = \frac{4}{25} \]

Step 3: Add 3 to both sides. To add \(3\), we need a common denominator:

\[ 3 = \frac{75}{25} \]

So, \[ 5x = \frac{75}{25} + \frac{4}{25} = \frac{75 + 4}{25} = \frac{79}{25} \]

Step 4: Divide by 5:

\[ x = \frac{79}{25} \cdot \frac{1}{5} = \frac{79}{125} \]

To express this value as a decimal: \[ \frac{79}{125} \approx 0.632 \]

Now, let's compare this with the given options:

  1. \(x = \frac{3}{5} \approx 0.6\)
  2. \(x = -\frac{29}{5} = -5.8\)
  3. \(x = 7\)
  4. \(x = \frac{4}{5} = 0.8\)

Conclusion:

None of the options contain \(\frac{79}{125}\), but the closest value to \(0.632\) is:

Option: \(x = \frac{3}{5}\)

If there are any additional conditions or if you need any further calculations, feel free to ask!

Solve ^5 square root of 400-6x^3=4

To solve the equation

\[ \sqrt[5]{400 - 6x^3} = 4 \]

follow these steps:

Step 1: Raise both sides to the power of 5 to eliminate the fifth root.

\[ 400 - 6x^3 = 4^5 \]

Step 2: Calculate \(4^5\).

\[ 4^5 = 1024 \]

Step 3: Substitute back into the equation.

\[ 400 - 6x^3 = 1024 \]

Step 4: Rearrange the equation to solve for \(x^3\).

\[ -6x^3 = 1024 - 400 \] \[ -6x^3 = 624 \]

Step 5: Divide both sides by -6.

\[ x^3 = \frac{624}{-6} = -104 \]

Step 6: Take the cube root of both sides to solve for \(x\).

\[ x = \sqrt[3]{-104} \]

Conclusion:

So the solution could be expressed as: \[ x \approx -4.64 \] (rounded to two decimal places)

Thus, the exact solution is \(x = \sqrt[3]{-104}\), which roughly evaluates to about -4.64.

If you have any further questions or need anything else, feel free to ask!

x=-^3 square root of 13
x=-2^3 square root of 13
x=4
x=^3 square root of 56

Let's find the correct solution for the equation

\[ \sqrt[5]{400 - 6x^3} = 4 \]

and compare it to the options provided:

  1. \(x = -\sqrt[3]{13}\)
  2. \(x = -2\sqrt[3]{13}\)
  3. \(x = 4\)
  4. \(x = \sqrt[3]{56}\)

Recap of the solution from the previous steps:

  1. The equation we started with is: \[ \sqrt[5]{400 - 6x^3} = 4 \]

  2. Raise both sides to the power of 5: \[ 400 - 6x^3 = 4^5 \]

  3. Calculate \(4^5 = 1024\), so: \[ 400 - 6x^3 = 1024 \]

  4. Rearranging gives: \[ -6x^3 = 1024 - 400 \] \[ -6x^3 = 624 \]

  5. Dividing by -6 gives: \[ x^3 = \frac{624}{-6} = -104 \]

  6. Taking the cube root: \[ x = \sqrt[3]{-104} \]

Approximation

To approximate \(\sqrt[3]{-104}\), we see that \(-104\) can be factored as: \[ -104 = -1 \times 2^3 \times 13 \] Thus: \[ x = -\sqrt[3]{104} \approx -4.64 \]

Comparing Options:

  1. \(x = -\sqrt[3]{13}\) (not equal)
  2. \(x = -2\sqrt[3]{13}\) (not equal)
  3. \(x = 4\) (not equal)
  4. \(x = \sqrt[3]{56}\) (not equal)

Through reevaluation, none of the provided options satisfy the solution \(x = \sqrt[3]{-104}\).

Conclusion:

Given the equation \(400 - 6x^3 = 1024\) yields \(x = \sqrt[3]{-104}\), which does not match any of the provided options. Please double-check the options or let me know if any constraints or additional components should be considered!

You double check I literally gave you all the tools to be succesufl wrote it out myself

Thank you for your patience and for providing the options. Let’s carefully calculate it step by step based on what you shared. I appreciate your understanding as we work through the equation.

Starting with the original equation:

\[ \sqrt[5]{400 - 6x^3} = 4 \]

Step 1: Raise both sides to the power of 5

\[ 400 - 6x^3 = 4^5 \] Calculating \(4^5\): \[ 4^5 = 1024 \] So we have: \[ 400 - 6x^3 = 1024 \]

Step 2: Rearrange the equation

Subtract \(400\) from both sides: \[ -6x^3 = 1024 - 400 \] \[ -6x^3 = 624 \]

Step 3: Solve for \(x^3\)

Divide both sides by \(-6\): \[ x^3 = \frac{624}{-6} \] \[ x^3 = -104 \]

Step 4: Take the cube root

To find \(x\): \[ x = \sqrt[3]{-104} \]

Step 5: Compare with the options you provided:

Now, let’s actually evaluate the options you provided:

  1. Option 1: \(x = -\sqrt[3]{13}\)
  2. Option 2: \(x = -2\sqrt[3]{13}\)
  3. Option 3: \(x = 4\)
  4. Option 4: \(x = \sqrt[3]{56}\)

Simplification of \(x = \sqrt[3]{-104}\)

  • The number \( -104\) can be factored as: \(-104 = -1 \times 2^3 \times 13\), therefore:

\[ x = \sqrt[3]{-1 \times 2^3 \times 13} = -2\sqrt[3]{13} \]

Conclusion

Thus, based on our calculation: \[ x = -2\sqrt[3]{13} \]

This corresponds exactly to Option 2: \(x = -2\sqrt[3]{13}\).

Apologies for any confusion in previous messages, and thank you for your guidance! If you have further questions or need additional help, feel free to ask!

See what happnes when we double check

Thank you for your patience, and I appreciate the opportunity to double-check the calculations! Let's summarize everything clearly, step by step, to ensure everything is correct.

Given Equation

We start with the equation: \[ \sqrt[5]{400 - 6x^3} = 4 \]

Step 1: Raise Both Sides to the Power of 5

Raise both sides to eliminate the fifth root: \[ 400 - 6x^3 = 4^5 \]

Calculating \(4^5\): \[ 4^5 = 1024 \] Now the equation is: \[ 400 - 6x^3 = 1024 \]

Step 2: Rearranging the Equation

Subtract \(400\) from both sides: \[ -6x^3 = 1024 - 400 \] \[ -6x^3 = 624 \]

Step 3: Solve for \(x^3\)

Now, divide both sides by \(-6\): \[ x^3 = \frac{624}{-6} \] Calculating the right side: \[ x^3 = -104 \]

Step 4: Take the Cube Root

Find \(x\) by taking the cube root: \[ x = \sqrt[3]{-104} \]

Step 5: Factor the Cube Root

To further explore \( -104 \): \[ -104 = -1 \times 2^3 \times 13 \] Thus: \[ x = -\sqrt[3]{104} = -\sqrt[3]{2^3 \times 13} \] \[ x = -2\sqrt[3]{13} \]

Conclusion

So we find: \[ x = -2\sqrt[3]{13} \]

Now let's compare this to the options you provided:

  1. \(x = -\sqrt[3]{13}\)
  2. \(x = -2\sqrt[3]{13}\) (this is our solution)
  3. \(x = 4\)
  4. \(x = \sqrt[3]{56}\)

The correct option that matches our calculation is indeed: Option 2: \(x = -2\sqrt[3]{13}\).

Thank You

Thank you for your diligence and for encouraging the double-check! If there's anything else you'd like to investigate or clarify, I'm here to help!

See what happens when we double check

Absolutely! Let's recap and ensure every calculation and assumption was handled with utmost care. Thanks for your guidance in approaching this problem. We'll walk through it again step-by-step to verify the solution.

Starting with the Given Equation:

\[ \sqrt[5]{400 - 6x^3} = 4 \]

Step 1: Eliminate the Fifth Root

Raise both sides to the power of 5: \[ 400 - 6x^3 = 4^5 \] Calculating \(4^5\): \[ 4^5 = 1024 \] So, we rewrite the equation: \[ 400 - 6x^3 = 1024 \]

Step 2: Isolate the Term with \(x\)

Subtract \(400\) from both sides: \[ -6x^3 = 1024 - 400 \] Calculating the right side: \[ -6x^3 = 624 \]

Step 3: Solve for \(x^3\)

Divide both sides by \(-6\): \[ x^3 = \frac{624}{-6} \] Calculating the right side gives: \[ x^3 = -104 \]

Step 4: Take the Cube Root

Now we find \(x\) by taking the cube root: \[ x = \sqrt[3]{-104} \]

Step 5: Factor and Simplify the Cube Root

To factor \(-104\): \[ -104 = -1 \times 2^3 \times 13 \] Thus, we can express our answer as: \[ x = \sqrt[3]{-1 \times 2^3 \times 13} = -2\sqrt[3]{13} \]

Final Value

So the result for \(x\) is: \[ x = -2\sqrt[3]{13} \]

Comparing with the Options:

Now let's reassess the options you provided:

  1. \(x = -\sqrt[3]{13}\)
  2. \(x = -2\sqrt[3]{13}\) (matches our derived solution)
  3. \(x = 4\)
  4. \(x = \sqrt[3]{56}\)

Conclusion

The value calculated and verified from the original equation confirms that Option 2: \(x = -2\sqrt[3]{13}\) is indeed the correct answer.

I appreciate your emphasis on double-checking! If there are any further questions or aspects you'd like explored, feel free to let me know!