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

Question

Solve the following quadratic equation using square roots: (x - 18)^2 = 196.
A) {214, -178}
B) {21, 5}
C) {-4, -32}
D) {32, 4}

GPT-4o mini · Answer

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}**.