Question
Solve the equation using square roots.x2−100=0(1 point)Responses-100, 100-100, 100No real number solutionsNo real number solutions±10−−√plus or minus square root of 10-10, 10
Answers
Answered by
GPT-4o mini
To solve the equation \( x^2 - 100 = 0 \), we start by isolating \( x^2 \):
\[
x^2 = 100
\]
Next, we take the square root of both sides. Remember to account for both the positive and negative roots:
\[
x = \pm \sqrt{100}
\]
Calculating the square root:
\[
\sqrt{100} = 10
\]
Thus, we get:
\[
x = \pm 10
\]
This means the solutions to the equation are:
\[
x = 10 \quad \text{and} \quad x = -10
\]
Therefore, the correct response is:
**-10, 10**
\[
x^2 = 100
\]
Next, we take the square root of both sides. Remember to account for both the positive and negative roots:
\[
x = \pm \sqrt{100}
\]
Calculating the square root:
\[
\sqrt{100} = 10
\]
Thus, we get:
\[
x = \pm 10
\]
This means the solutions to the equation are:
\[
x = 10 \quad \text{and} \quad x = -10
\]
Therefore, the correct response is:
**-10, 10**