To determine whether a given value of \( x \) is a solution to the quadratic equation \( x^2 + 20x = 69 \), we can rearrange the equation as follows:
\[ x^2 + 20x - 69 = 0 \]
Now, let's test some values.
Here are the steps for testing a value of \( x \):
- Substitute the value of \( x \) into the left side of the equation.
- Calculate the result.
- If the result equals zero, then that value is a solution.
Let's consider the following possible values for testing. Since no specific values were given, I'll demonstrate the process with a few arbitrary values, and you can substitute the specific values provided in your problem.
Testing Values
-
Test \( x = -30 \): \[ (-30)^2 + 20(-30) - 69 = 900 - 600 - 69 = 231 \quad (\text{not a solution}) \]
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Test \( x = -25 \): \[ (-25)^2 + 20(-25) - 69 = 625 - 500 - 69 = 56 \quad (\text{not a solution}) \]
-
Test \( x = -20 \): \[ (-20)^2 + 20(-20) - 69 = 400 - 400 - 69 = -69 \quad (\text{not a solution}) \]
-
Test \( x = -15 \): \[ (-15)^2 + 20(-15) - 69 = 225 - 300 - 69 = -144 \quad (\text{not a solution}) \]
-
Test \( x = -10 \): \[ (-10)^2 + 20(-10) - 69 = 100 - 200 - 69 = -169 \quad (\text{not a solution}) \]
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Test \( x = -5 \): \[ (-5)^2 + 20(-5) - 69 = 25 - 100 - 69 = -144 \quad (\text{not a solution}) \]
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Test \( x = 0 \): \[ 0^2 + 20(0) - 69 = 0 - 69 = -69 \quad (\text{not a solution}) \]
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Test \( x = 3 \): \[ 3^2 + 20(3) - 69 = 9 + 60 - 69 = 0 \quad (\text{this is a solution}) \]
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Test \( x = 5 \): \[ 5^2 + 20(5) - 69 = 25 + 100 - 69 = 56 \quad (\text{not a solution}) \]
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Test \( x = 6 \): \[ 6^2 + 20(6) - 69 = 36 + 120 - 69 = 87 \quad (\text{not a solution}) \]
Conclusion
From our tests, \( x = 3 \) satisfies the equation and is the only value in the solution set among the values we tested.
Therefore, only \( x = 3 \) is in the solution set. You can replace \( x = 3 \) with whatever specific values you have to check against the equation.
If you have specific values to check, please provide them, and I can assist further.