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

Question

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

GPT-4o mini · Answer

To solve the quadratic equation $(x - 18)^2 = 196$, we will take the square root of both sides. 1. Start by taking the square root of both sides: $$ x - 18 = \pm \sqrt{196} $$ Since $\sqrt{196} = 14$, we have: $$ x - 18 = \pm 14 $$ 2. Now we can split this into two equations: $$ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 $$ 3. Solve the first equation: $$ x - 18 = 14 $$ $$ x = 14 + 18 $$ $$ x = 32 $$ 4. Solve the second equation: $$ x - 18 = -14 $$ $$ x = -14 + 18 $$ $$ x = 4 $$ The solutions to the quadratic equation $(x - 18)^2 = 196$ are $x = 32$ and $x = 4$. Thus, the answer is: $\{32, 4\}$