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}

Answer 1

To solve the quadratic equation (x-18)^2 = 196, we can start by taking the square root of both sides:

√((x-18)^2) = √196

Simplifying the left side, we have:

|x-18| = 14

Next, we can split the equation into two separate equations:

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

Solving the first equation, we can add 18 to both sides:

x = 14 + 18

x = 32

Solving the second equation, we can add 18 to both sides:

x = -14 + 18

x = 4

Therefore, the solutions to the quadratic equation (x-18)^2 = 196 are {32, 4}.