Question

Complete the square to identify the two values that solve the following quadratic equation: x^2−16x−13=4 .(1 point)
x=_

Answer 1

I need one answer

Answer 2

To solve the equation \( x^2 - 16x - 13 = 4 \) by completing the square, we start by rearranging the equation to set it to zero:

\[
x^2 - 16x - 13 - 4 = 0
\]

This simplifies to:

\[
x^2 - 16x - 17 = 0
\]

Next, we can move the constant term to the other side:

\[
x^2 - 16x = 17
\]

Now, we complete the square. To do this, take half of the coefficient of \( x \) (which is \(-16\)), square it, and add it to both sides. Half of \(-16\) is \(-8\), and squaring it gives \(64\):

\[
x^2 - 16x + 64 = 17 + 64
\]

This simplifies to:

\[
(x - 8)^2 = 81
\]

Now, we take the square root of both sides:

\[
x - 8 = \pm 9
\]

This results in two equations:

1. \( x - 8 = 9 \) \\
\( x = 9 + 8 = 17 \)

2. \( x - 8 = -9 \) \\
\( x = -9 + 8 = -1 \)

Thus, the two values that solve the equation are:

\[
x = 17 \quad \text{and} \quad x = -1
\]

So, the final answers for \( x \) are:

\[
x = 17, \quad x = -1
\]

Answer 3

The two values that solve the equation \( x^2 - 16x - 13 = 4 \) are:

\( x = 17 \) and \( x = -1 \).

If you need just one answer, you can select either:

**\( x = 17 \)** or **\( x = -1 \)**.

Please let me know if you need any further help!