Use inspection to solve the equation x² = 81, then select the complete solution set below. If there are no real solutions, select "There are no real solutions." (1 point)

Question

{-9}
There are no real solutions.
{9}
{-9,9}

Answer 1

To solve the equation \( x^2 = 81 \) by inspection, we look for values of \( x \) that, when squared, equal 81.

The square root of 81 is 9, so we find two possible solutions:

1. \( x = 9 \)
2. \( x = -9 \)

Thus, the complete solution set is:

\({-9, 9}\)

So the correct answer is \({-9, 9}\).

Answer 2

Use inspection to solve the equation x² = 81, then select the complete solution set below. If there are no real solutions, select "There are no real solutions." (1 point)

{-9}
There are no real solutions.
{9}
{-9,9}

Answer 3

For the equation \( x^2 = 81 \), we can determine the values of \( x \) by inspection.

The square roots of 81 are:

1. \( x = 9 \)
2. \( x = -9 \)

Thus, the complete solution set is:

\({-9, 9}\)

So, the correct choice is:

\({-9, 9}\)

Answer 4

Use inspection to solve the equation x² = 36/169, then select the correct solution set below. If there are no real solutions, select "There are no real solutions."
There are no real solutions.
{-6/13 * 6/13}
{-6/13}
{6/13}

Answer 5

To solve the equation \( x^2 = \frac{36}{169} \) by inspection, we can take the square root of both sides.

The square root of \( \frac{36}{169} \) is:

\[ x = \frac{6}{13} \quad \text{or} \quad x = -\frac{6}{13} \]

Therefore, the complete solution set is:

\(\left{-\frac{6}{13}, \frac{6}{13}\right}\)

Since that option is not listed, we should select:

• \(-\frac{6}{13}\) (which is one of the solutions)
• \(\frac{6}{13}\) (which is the other solution)

The correct solution set includes both \(-\frac{6}{13}\) and \(\frac{6}{13}\). So, you can consider both or check which one is most applicable according to the choices provided. If you're looking for which choice fits the solution set accurately based on the format:

The correct concise choices are:

• {-6/13}
• {6/13}

However, if available, a selection reflecting both values would be ideal. If you must pick only one based on the options given without having both, please note:

The listed options do not contain the correct solution set in full. Therefore, you could argue if limited to one, select either \(-\frac{6}{13}\) or \(\frac{6}{13}\) based on your scenario.

Final Choice Depending on Further Information from Provided Options: Either option standing alone or instructing that multiple solutions should be considered.

Answer 6

so which answer is it?

Answer 7

Given the options you provided, the correct answers based on solving the equation \( x^2 = \frac{36}{169} \) are:

1. \( x = \frac{6}{13} \)
2. \( x = -\frac{6}{13} \)

However, the option that resembles both solutions simultaneously is not provided. Based on the selections given:

• Select \({-\frac{6}{13}}\)
• Select \({6/13}\)

If you have to choose one answer from your options without being able to represent both, you could choose either. If you only get to select one, I would suggest selecting \({6/13}\) as it reflects a positive value since both solutions should ideally be considered collectively but typically only one solution appears on a multiple-choice list.

If you intend to reflect both values as accurately as possible based on traditional mathematical representation, you'd aim for indicating that \({-\frac{6}{13}, \frac{6}{13}}\) is the full solution set; however, strictly speaking, based on the answers you've shown, go with \({6/13}\) as a solid pick since it represents a valid solution.

Answer 8

A. There are no real solutions.
B. {-6/13 * 6/13}
C. {-6/13}
D. {6/13}

Answer 9

Based on solving the equation \( x^2 = \frac{36}{169} \), the correct solution set includes both solutions:

1. \( x = \frac{6}{13} \)
2. \( x = -\frac{6}{13} \)

From the options given:

A. There are no real solutions.
B. {-6/13 * 6/13}
C. {-6/13}
D. {6/13}

The correct answer is:

• D. {6/13}

However, note that the complete solution set should ideally be {-6/13, 6/13}. Since that's not an option, {6/13} is the correct choice among the provided answers.

Answer 10

Solve the following quadratic equation using square roots: (x - 18)^2 = 196
{32,4}
{214, -178}
{-4, -32}
{21,5}

Answer 11

To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, we follow these steps:

1. Take the square root of both sides:
   \[ x - 18 = \pm \sqrt{196} \]

2. Calculate \(\sqrt{196}\):
   Since \(196 = 14^2\), we have: \[ \sqrt{196} = 14 \]

3. Set up the equations: \[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]

4. Solve for \(x\):

   • For \(x - 18 = 14\): \[ x = 14 + 18 = 32 \]
   • For \(x - 18 = -14\): \[ x = -14 + 18 = 4 \]

Thus, the solutions to the equation are \(x = 32\) and \(x = 4\).

Therefore, the correct answer is: {32, 4}.

Answer 12

Solve the following quadratic equation using square roots: (x - 18)^2 = 196

{32,4}
{214, -178}
{-4, -32}
{21,5}

Answer 13

To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, we can follow these steps:

1. Take the square root of both sides: \[ x - 18 = \pm \sqrt{196} \]

2. Calculate \(\sqrt{196}\): \[ \sqrt{196} = 14 \]

3. Set up the two equations:

   • \(x - 18 = 14\)
   • \(x - 18 = -14\)

4. Solve for \(x\) in each case:

   • For \(x - 18 = 14\): \[ x = 14 + 18 = 32 \]
   • For \(x - 18 = -14\): \[ x = -14 + 18 = 4 \]

Thus, the solutions to the equation are \(x = 32\) and \(x = 4\).

The correct answer is: {32, 4}.

Answer 14

Solve the following quadratic equation using square roots: ((x + 6)^2)/2 = 8
{10, -22}
{-1.17, -6.83}
{-0.34, -11.66}
{-2, -10}

Answer 15

To solve the quadratic equation \(\frac{(x + 6)^2}{2} = 8\) using square roots, follow these steps:

1. Multiply both sides by 2 to eliminate the fraction: \[ (x + 6)^2 = 16 \]

2. Take the square root of both sides: \[ x + 6 = \pm \sqrt{16} \]

3. Calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \]

4. Set up the two equations:

   • \(x + 6 = 4\)
   • \(x + 6 = -4\)

5. Solve for \(x\) in each case:

   • For \(x + 6 = 4\): \[ x = 4 - 6 = -2 \]
   • For \(x + 6 = -4\): \[ x = -4 - 6 = -10 \]

Thus, the solutions to the equation are \(x = -2\) and \(x = -10\).

The correct answer is: {-2, -10}.

Answer 16

Solve the following quadratic equation using square roots: ((x + 6)^2)/2 = 8

{10, -22}
{-1.17, -6.83}
{-0.34, -11.66}
{-2, -10}

Answer 17

To solve the equation \(\frac{(x + 6)^2}{2} = 8\) using square roots, follow these steps:

1. Multiply both sides by 2 to eliminate the fraction: \[ (x + 6)^2 = 16 \]

2. Take the square root of both sides: \[ x + 6 = \pm \sqrt{16} \]

3. Calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \]

4. Set up the two equations:

   • \(x + 6 = 4\)
   • \(x + 6 = -4\)

5. Solve for \(x\) in each case:

   • For \(x + 6 = 4\): \[ x = 4 - 6 = -2 \]
   • For \(x + 6 = -4\): \[ x = -4 - 6 = -10 \]

Thus, the solutions to the equation are \(x = -2\) and \(x = -10\).

The correct answer is: {-2, -10}.

Answer 18

Solve the following quadratic equation using square roots: (x + 36)^2 - 38 = 251.
{253, -325)
{17.84, -13.84}
{53, 19}
{-19,-53}

Answer 19

To solve the quadratic equation \((x + 36)^2 - 38 = 251\), follow these steps:

1. Isolate the squared term: \[ (x + 36)^2 = 251 + 38 \] \[ (x + 36)^2 = 289 \]

2. Take the square root of both sides: \[ x + 36 = \pm \sqrt{289} \]

3. Calculate \(\sqrt{289}\): \[ \sqrt{289} = 17 \]

4. Set up the two equations:

   • \(x + 36 = 17\)
   • \(x + 36 = -17\)

5. Solve for \(x\) in each case:

   • For \(x + 36 = 17\): \[ x = 17 - 36 = -19 \]
   • For \(x + 36 = -17\): \[ x = -17 - 36 = -53 \]

Thus, the solutions to the equation are \(x = -19\) and \(x = -53\).

The correct answer is: {-19, -53}.

Answer 20

Solve the following quadratic equation using square roots: (x + 36)^2 - 38 = 251.

{253, -325)
{17.84, -13.84}
{53, 19}
{-19,-53}

Answer 21

To solve the quadratic equation \((x + 36)^2 - 38 = 251\), we'll follow these steps:

1. Isolate the squared term: \[ (x + 36)^2 = 251 + 38 \] \[ (x + 36)^2 = 289 \]

2. Take the square root of both sides: \[ x + 36 = \pm \sqrt{289} \]

3. Calculate \(\sqrt{289}\): \[ \sqrt{289} = 17 \]

4. Set up the two equations:

   • \(x + 36 = 17\)
   • \(x + 36 = -17\)

5. Solve for \(x\) in each case:

   • For \(x + 36 = 17\): \[ x = 17 - 36 = -19 \]
   • For \(x + 36 = -17\): \[ x = -17 - 36 = -53 \]

Thus, the solutions to the equation are \(x = -19\) and \(x = -53\).

The correct answer is: {-19, -53}.

Answer 22

Solve x^2 = 36 by inspection. There are two real solutions. Enter the lesser number first.

Answer 23

To solve the equation \(x^2 = 36\) by inspection, we can find the square roots of 36.

The square roots are:

1. \(x = 6\)
2. \(x = -6\)

The solutions are \(-6\) and \(6\).

Entering the lesser number first, the complete solution set is: \(-6, 6\).

Answer 24

Solve x^2 = 16/25 by inspection. There are two real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

Answer 25

To solve the equation \(x^2 = \frac{16}{25}\) by inspection, we take the square root of both sides.

The square roots are:

1. \(x = \frac{4}{5}\)
2. \(x = -\frac{4}{5}\)

Listing the solutions and entering the lesser number first, the complete solution set in simplest fraction form is: \(-\frac{4}{5}, \frac{4}{5}\).

Answer 26

Solve the following quadratic equation using square roots: (x + 3)^2 = 36

Answer 27

To solve the quadratic equation \((x + 3)^2 = 36\) using square roots, follow these steps:

1. Take the square root of both sides: \[ x + 3 = \pm \sqrt{36} \]

2. Calculate \(\sqrt{36}\): \[ \sqrt{36} = 6 \]

3. Set up the two equations:

   • \(x + 3 = 6\)
   • \(x + 3 = -6\)

4. Solve for \(x\) in each case:

   • For \(x + 3 = 6\): \[ x = 6 - 3 = 3 \]
   • For \(x + 3 = -6\): \[ x = -6 - 3 = -9 \]

Thus, the solutions to the equation are \(x = 3\) and \(x = -9\).

So, the final answers are: \[ 3, -9 \]

Answer 28

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x - 6)^2 = 51

Answer 29

To solve the equation \((x - 6)^2 = 51\) using square roots, follow these steps:

1. Take the square root of both sides: \[ x - 6 = \pm \sqrt{51} \]

2. Calculate \(\sqrt{51}\): The square root of 51 is approximately: \[ \sqrt{51} \approx 7.1414 \quad (\text{rounded to 4 decimal places}) \]

3. Set up the two equations:

   • \(x - 6 = \sqrt{51}\)
   • \(x - 6 = -\sqrt{51}\)

4. Solve for \(x\) in each case:

   • For \(x - 6 = \sqrt{51}\): \[ x = 6 + \sqrt{51} \approx 6 + 7.1414 \approx 13.1414 \] When rounded to the nearest hundredth, this is: \[ x \approx 13.14 \]

   • For \(x - 6 = -\sqrt{51}\): \[ x = 6 - \sqrt{51} \approx 6 - 7.1414 \approx -1.1414 \] When rounded to the nearest hundredth, this is: \[ x \approx -1.14 \]

Thus, the solutions to the equation \((x - 6)^2 = 51\) are approximately: \[ \boxed{13.14} \quad \text{and} \quad \boxed{-1.14} \]

Answer 30

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: ((x + 16)^2)/9 = 7

Answer 31

To solve the equation \(\frac{(x + 16)^2}{9} = 7\) using square roots, follow these steps:

1. Multiply both sides by 9 to eliminate the fraction: \[ (x + 16)^2 = 63 \]

2. Take the square root of both sides: \[ x + 16 = \pm \sqrt{63} \]

3. Calculate \(\sqrt{63}\): \[ \sqrt{63} \approx 7.937 (rounded to three decimal places) \]

4. Set up the two equations:

   • \(x + 16 = \sqrt{63}\)
   • \(x + 16 = -\sqrt{63}\)

5. Solve for \(x\) in each case:

   • For \(x + 16 = \sqrt{63}\): \[ x = \sqrt{63} - 16 \approx 7.937 - 16 \approx -8.063 \] When rounded to the nearest hundredth, this is: \[ x \approx -8.06 \]

   • For \(x + 16 = -\sqrt{63}\): \[ x = -\sqrt{63} - 16 \approx -7.937 - 16 \approx -23.937 \] When rounded to the nearest hundredth, this is: \[ x \approx -23.94 \]

Thus, the solutions to the equation \(\frac{(x + 16)^2}{9} = 7\) are approximately: \[ \boxed{-8.06} \quad \text{and} \quad \boxed{-23.94} \]