Question
Solving Simple Quadratic Equations Quick Check
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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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Answers
GPT-4o mini
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}**.
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}**.