Question

hich equation has the same solution as x, squared, minus, 16, x, minus, 9, equals, minus, 8x
2
−16x−9=−8?
Answer
Attempt 3 out of 3
Multiple Choice Answers
left parenthesis, x, minus, 8, right parenthesis, squared, equals, minus, 63(x−8)
2
=−63
left parenthesis, x, plus, 8, right parenthesis, squared, equals, minus, 63(x+8)
2
=−63
left parenthesis, x, plus, 8, right parenthesis, squared, equals, 65(x+8)
2
=65
left parenthesis, x, minus, 8, right parenthesis, squared, equals, 65(x−8)
2
=65

Answer 1

To solve the equation \( x^2 - 16x - 9 = -8 \), we first rewrite it in standard form by adding 8 to both sides:

\[
x^2 - 16x - 1 = 0
\]

Next, we can use the method of completing the square. To complete the square, we look at the coefficient of \( x \), which is -16. We take half of this value and square it:

\[
\left( \frac{-16}{2} \right)^2 = (-8)^2 = 64
\]

Now, we add and subtract 64 to the left side of the equation:

\[
x^2 - 16x + 64 - 64 - 1 = 0
\]

This can be rewritten as:

\[
(x - 8)^2 - 65 = 0
\]

Now, isolating \( (x - 8)^2 \):

\[
(x - 8)^2 = 65
\]

Now, we can match this with the provided answer choices. The correct equivalent equation is:

\[
(x - 8)^2 = 65
\]

Thus, the answer is:

\[
\text{left parenthesis, } (x - 8) \text{, right parenthesis, squared, equals, 65, }(x - 8)^2 = 65
\]