Question

For the quadratic equation x2+20x=69
𝑥
2
+
20
𝑥
=
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=
𝑥
=
is in the solution set.

Answer 1

Answer

Answer 2

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 \( x \):

1. Substitute the value of \( x \) into the left side of the equation.
2. Calculate the result.
3. 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

1. **Test \( x = -30 \)**:
\[
(-30)^2 + 20(-30) - 69 = 900 - 600 - 69 = 231 \quad (\text{not a solution})
\]

2. **Test \( x = -25 \)**:
\[
(-25)^2 + 20(-25) - 69 = 625 - 500 - 69 = 56 \quad (\text{not a solution})
\]

3. **Test \( x = -20 \)**:
\[
(-20)^2 + 20(-20) - 69 = 400 - 400 - 69 = -69 \quad (\text{not a solution})
\]

4. **Test \( x = -15 \)**:
\[
(-15)^2 + 20(-15) - 69 = 225 - 300 - 69 = -144 \quad (\text{not a solution})
\]

5. **Test \( x = -10 \)**:
\[
(-10)^2 + 20(-10) - 69 = 100 - 200 - 69 = -169 \quad (\text{not a solution})
\]

6. **Test \( x = -5 \)**:
\[
(-5)^2 + 20(-5) - 69 = 25 - 100 - 69 = -144 \quad (\text{not a solution})
\]

7. **Test \( x = 0 \)**:
\[
0^2 + 20(0) - 69 = 0 - 69 = -69 \quad (\text{not a solution})
\]

8. **Test \( x = 3 \)**:
\[
3^2 + 20(3) - 69 = 9 + 60 - 69 = 0 \quad (\text{this is a solution})
\]

9. **Test \( x = 5 \)**:
\[
5^2 + 20(5) - 69 = 25 + 100 - 69 = 56 \quad (\text{not a solution})
\]

10. **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.

Answer 3

Only \( x = 3 \) is in the solution set for the equation \( x^2 + 20x = 69 \).