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

Question

A) {214, -178}
B) {21, 5}
C) {-4, -32}
D) {32, 4}

Answer 1

To solve the equation \((x - 18)^2 = 196\) using square roots, we proceed as follows:

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 solve for \(x\):

   • Case 1: \[ x - 18 = 14 \] Solving for \(x\): \[ x = 14 + 18 = 32 \]

   • Case 2: \[ x - 18 = -14 \] Solving for \(x\): \[ x = -14 + 18 = 4 \]

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

Thus, the solution set is \({32, 4}\).

The correct answer is:

D) {32, 4}.