Question

Solve the following quadratic equation using square roots: (−9+(x−3)2)/−4=−4
.(1 point)

Answer 1

To solve the equation \(\frac{-9 + (x - 3)^2}{-4} = -4\), we first eliminate the fraction by multiplying both sides by \(-4\):

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

Next, we isolate \((x - 3)^2\) by adding \(9\) to both sides of the equation:

\[
(x - 3)^2 = 16 + 9
\]
\[
(x - 3)^2 = 25
\]

Now, we can solve for \(x - 3\) by taking the square root of both sides. Remember to consider both the positive and negative roots:

\[
x - 3 = \pm 5
\]

This gives us two cases to consider:

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

Now we solve each case:

1. For \(x - 3 = 5\):
\[
x = 5 + 3 = 8
\]

2. For \(x - 3 = -5\):
\[
x = -5 + 3 = -2
\]

Thus, the solutions to the quadratic equation are:

\[
x = 8 \quad \text{and} \quad x = -2
\]