Question

Solve the quadratic equation below using square roots.

(x−4)2=25


(1 point)
Responses

{−29−−√, 29−−√}
{−29−−√, 29−−√}

{−2, 6}
{−2, 6}

{−3, 7}
{−3, 7}

{−1, 9}

Answer 1

To solve the quadratic equation \((x−4)^2=25\) using square roots, we start by taking the square root of both sides:

\[
x - 4 = \pm 5
\]

This gives us two separate equations to solve:

1. \(x - 4 = 5\)
2. \(x - 4 = -5\)

Now, solving these equations:

### For the first equation:
\[
x - 4 = 5
\]
Adding 4 to both sides:
\[
x = 5 + 4 = 9
\]

### For the second equation:
\[
x - 4 = -5
\]
Adding 4 to both sides:
\[
x = -5 + 4 = -1
\]

So, the solutions are:
\[
x = 9 \quad \text{and} \quad x = -1
\]

Thus, the answer is \(\{-1, 9\}\).