Question

solve the following quadratic equation using square roots -9+(x-3)^2/-4 = -4
{28,-22}
{8,-2}
{16,-10}
{2,-8}

Answer 1

To solve the quadratic equation using square roots, we start with the given equation:

\[
\frac{-9 + (x - 3)^2}{-4} = -4
\]

First, we can multiply both sides of the equation by -4 to eliminate the fraction:

\[
-9 + (x - 3)^2 = 16
\]

Next, we'll move -9 to the other side of the equation:

\[
(x - 3)^2 = 16 + 9
\]

\[
(x - 3)^2 = 25
\]

Now, we take the square root of both sides:

\[
x - 3 = \pm 5
\]

This gives us two equations to solve:

1. \(x - 3 = 5\)
2. \(x - 3 = -5\)

Solving the first equation:

\[
x = 5 + 3 = 8
\]

Solving the second equation:

\[
x = -5 + 3 = -2
\]

Therefore, the solutions to the equation are:

\[
\{8, -2\}
\]

The correct answer is:

\(\{8, -2\}\)