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

Question

Responses

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

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

{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. Calculate $\sqrt{196}$: $$\sqrt{196}=14$$

3. Now set up the two equations: $$x-18=14\text{and}x-18=-14$$

4. Solve the first equation: $$x-18=14⟹x=14+18=32$$

5. Solve the second equation: $$x-18=-14⟹x=-14+18=4$$

Thus, the solutions to the equation are: $$32,4$$

So the correct response is: $$32,4$$