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

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

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

​ {−4,−32}

Answer 1

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

1. Take the square root: \[ x - 18 = \pm \sqrt{196} \]

2. Calculate \(\sqrt{196}\): \[ \sqrt{196} = 14 \]

So we have: \[ x - 18 = \pm 14 \]

This gives us two equations to solve:

1. \(x - 18 = 14\)
2. \(x - 18 = -14\)

For the first equation: \[ x - 18 = 14 \] \[ x = 14 + 18 \] \[ x = 32 \]

For the second equation: \[ x - 18 = -14 \] \[ x = -14 + 18 \] \[ x = 4 \]

Thus, the solutions to the equation are: \[ x = 32 \quad \text{and} \quad x = 4 \]

So the answer is: \[ {32, 4} \]