Question

Solve the following quadratic equation using square roots:
(
x
−
18
)
2
=
196
.
(1 point) {−4, − 32}
{214, − 178}
{32, 4}
{21, 5}

Answer 1

To solve the quadratic equation \((x - 18)^2 = 196\), we will use the method of square roots.

1. Take the square root of both sides of the equation:

\[
x - 18 = \pm \sqrt{196}
\]

2. Calculate \(\sqrt{196}\):

\[
\sqrt{196} = 14
\]

3. Now we have two cases to consider:

**Case 1:**
\[
x - 18 = 14
\]
\[
x = 14 + 18 = 32
\]

**Case 2:**
\[
x - 18 = -14
\]
\[
x = -14 + 18 = 4
\]

So the solutions to the equation are:

\[
x = 32 \quad \text{and} \quad x = 4
\]

Thus, the final answer is:

\[
\{32, 4\}
\]