Question

Solve the following quadratic equation using square roots: −9+(x−3)2=16
(1 point)
Responses

{28, -22}
{28, -22}

{2, -8}
{2, -8}

{16, -10}
{16, -10}

{8, -2}

Answer 1

To solve the equation \(-9 + (x - 3)^2 = 16\), let's start by isolating the squared term.

1. Add 9 to both sides:
\[
(x - 3)^2 = 16 + 9
\]
\[
(x - 3)^2 = 25
\]

2. Now, take the square root of both sides:
\[
x - 3 = \pm 5
\]

3. Solve for \(x\):
- For the positive case:
\[
x - 3 = 5 \implies x = 5 + 3 \implies x = 8
\]
- For the negative case:
\[
x - 3 = -5 \implies x = -5 + 3 \implies x = -2
\]

Thus, the solutions for the equation are \(x = 8\) and \(x = -2\).

So the answer is \(\{8, -2\}\).