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

Question

Responses

{214,−178}
left brace 214 comma negative 178 right brace

{32,4}
left brace 32 comma 4 right brace

{21,5}
left brace 21 comma 5 right brace

​ {−4,−32}
​ left brace negative 4 comma negative 32 right brace

Answer 1

To solve the quadratic equation (x-18)^2 = 196 using square roots, we first need to take the square root of both sides of the equation. This will give us two possible solutions:

(x-18) = ±√196

Simplifying, we have:

(x-18) = ±14

Now we can solve for x:

x-18 = 14 or x-18 = -14

Adding 18 to both sides, we get:

x = 32 or x = 4

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