Question

Solve equation with square roots: (x - 18)^2 = 196

Answer 1

To solve the equation \((x - 18)^2 = 196\), we can start by taking the square root of both sides. Remember that when we take the square root, we need to consider both the positive and negative roots.

1. Take the square root of both sides:
\[
x - 18 = \pm \sqrt{196}
\]

2. Calculate \(\sqrt{196}\):
\[
\sqrt{196} = 14
\]

3. Now we have:
\[
x - 18 = 14 \quad \text{or} \quad x - 18 = -14
\]

4. Solve each equation separately:

- For \(x - 18 = 14\):
\[
x = 14 + 18 = 32
\]

- For \(x - 18 = -14\):
\[
x = -14 + 18 = 4
\]

5. Thus, the solutions to the equation \((x - 18)^2 = 196\) are:
\[
x = 32 \quad \text{and} \quad x = 4
\]

Therefore, the solutions are \(x = 32\) and \(x = 4\).