Solving Simple Quadratic Equations Quick Check

Question

3 of 53 of 5 Items
Question
Solve the following quadratic equation using square roots: (x−18)2=196.(1 point)
Responses

{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

{214,−178}
left brace 214 comma negative 178 right brace
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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. Set up the two equations from the result: \[ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 \]

4. Solve each equation:

   • For \(x - 18 = 14\): \[ x = 18 + 14 = 32 \]

   • For \(x - 18 = -14\): \[ x = 18 - 14 = 4 \]

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

Thus, the correct answer is \({32, 4}\).

So the answer is: {32, 4}.