Question
Solve the quadratic equation using square roots: (x-18)^2 =196
Answers
Answered by
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. Remember to consider both the positive and negative square roots:
\[
x - 18 = \pm \sqrt{196}
\]
2. Calculate the square root of 196:
\[
\sqrt{196} = 14
\]
So the equation becomes:
\[
x - 18 = \pm 14
\]
3. Now, split this into two separate equations:
- First equation:
\[
x - 18 = 14
\]
Adding 18 to both sides gives:
\[
x = 14 + 18 = 32
\]
- Second equation:
\[
x - 18 = -14
\]
Adding 18 to both sides gives:
\[
x = -14 + 18 = 4
\]
4. Therefore, the solutions to the equation \((x - 18)^2 = 196\) are:
\[
x = 32 \quad \text{and} \quad x = 4
\]
So, \(x = 32\) and \(x = 4\) are the final answers.
1. Take the square root of both sides. Remember to consider both the positive and negative square roots:
\[
x - 18 = \pm \sqrt{196}
\]
2. Calculate the square root of 196:
\[
\sqrt{196} = 14
\]
So the equation becomes:
\[
x - 18 = \pm 14
\]
3. Now, split this into two separate equations:
- First equation:
\[
x - 18 = 14
\]
Adding 18 to both sides gives:
\[
x = 14 + 18 = 32
\]
- Second equation:
\[
x - 18 = -14
\]
Adding 18 to both sides gives:
\[
x = -14 + 18 = 4
\]
4. Therefore, the solutions to the equation \((x - 18)^2 = 196\) are:
\[
x = 32 \quad \text{and} \quad x = 4
\]
So, \(x = 32\) and \(x = 4\) are the final answers.
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