Question

Solve the following quadratic equation using square roots: ( x -18 )^2 = 196.

A: { 32,4}

B: { 214, -178}

C: { -4, -32}

D: { 21,5}

Answer 1

To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, follow these steps:

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

2. Calculate the square root:
\[
\sqrt{196} = 14
\]
Therefore, we have:
\[
x - 18 = 14 \quad \text{or} \quad x - 18 = -14
\]

3. Solve for \(x\) in both cases:

- For the first equation:
\[
x - 18 = 14 \implies x = 14 + 18 \implies x = 32
\]

- For the second equation:
\[
x - 18 = -14 \implies x = -14 + 18 \implies x = 4
\]

Thus, the solutions to the equation are \(x = 32\) and \(x = 4\).

Therefore, the answer is:
**A: {32, 4}**.