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

Question

(
𝑥
−
18
)
2
=
196
.(1 point)
Responses

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

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

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

{21,5}

Answer 1

To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, follow these steps:

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

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

3. Thus, we have two equations to solve: \[ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 \]

4. Solve the first equation: \[ x - 18 = 14 \implies x = 14 + 18 = 32 \]

5. Solve the second equation: \[ x - 18 = -14 \implies x = -14 + 18 = 4 \]

The solutions are: \[ x = 32 \quad \text{and} \quad x = 4 \]

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