Question

For the quadratic equation x^2+20x=69 , complete the table by testing each of the given values to determine whether it is a solution. Identify which one of these values is in the solution set. (1 point) Only x=□ is in the solution set

Answer 1

To determine if a given value is a solution to the quadratic equation \(x^2 + 20x = 69\), we can first rewrite the equation in standard form:

\[
x^2 + 20x - 69 = 0
\]

Next, we will assess whether each provided value, let's say \(x = a\), satisfies the equation by substituting it in:

\[
a^2 + 20a - 69 = 0
\]

For demonstration, I will verify if some common values could be solutions. If you have specific values to test, please provide them, and I will adjust accordingly.

Here’s how you would test some arbitrary values to determine if they satisfy the equation:

1. For example, test \(x = -30\):
\[
(-30)^2 + 20(-30) - 69 = 900 - 600 - 69 = 231 \quad (\text{Not a solution})
\]

2. Next, test \(x = -10\):
\[
(-10)^2 + 20(-10) - 69 = 100 - 200 - 69 = -169 \quad (\text{Not a solution})
\]

3. Next, test \(x = -3\):
\[
(-3)^2 + 20(-3) - 69 = 9 - 60 - 69 = -120 \quad (\text{Not a solution})
\]

4. Finally, test \(x = -1\):
\[
(-1)^2 + 20(-1) - 69 = 1 - 20 - 69 = -88 \quad (\text{Not a solution})
\]

5. Now let's test \(x = 3\):
\[
(3)^2 + 20(3) - 69 = 9 + 60 - 69 = 0 \quad (\text{This is a solution})
\]

Identifying the correct solution: After testing all relevant values, only \(x = 3\) satisfies the equation.

So, if this matches one of your test values, you can fill in the blank with \(3\).

The answer would then be:

Only \(x = \boxed{3}\) is in the solution set.

If you have other specific values to test or further instructions, please provide them, and I'll help you through it!