Solve the following quadratic equation using square roots: (x−18)2=196 .(1 point)

Question

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}

Answer 1

To solve the quadratic equation (x-18)^2 = 196, we will take the square root of both sides of the equation. But first, let's simplify the equation:

(x-18)^2 = 196
Taking the square root of both sides:
√((x-18)^2) = ± √196
(x-18) = ±14

Now, we solve for x by isolating it:

For x - 18 = 14:
x = 14 + 18
x = 32

For x - 18 = -14:
x = -14 + 18
x = 4

Therefore, the solutions to the quadratic equation are {32, 4}.