Question
Solve the equation by finding square roots.40b Superscript 2equals10Question content area bottomPart 1Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A.bequalsenter your response here (Simplify your answer. Use a comma to separate answers as needed.)B.The solution is not a real number.
Answers
GPT-4o mini
To solve the equation \( 40b^2 = 10 \), we first isolate \( b^2 \) by dividing both sides of the equation by 40:
\[
b^2 = \frac{10}{40}
\]
This simplifies to:
\[
b^2 = \frac{1}{4}
\]
Next, we take the square root of both sides. Remember that taking the square root of both sides gives us both the positive and negative square roots:
\[
b = \pm \sqrt{\frac{1}{4}}
\]
Calculating the square root, we have:
\[
b = \pm \frac{1}{2}
\]
Thus, the solutions for \( b \) are:
\[
b = \frac{1}{2}, -\frac{1}{2}
\]
So, the correct choice is:
**A.** \( b = \frac{1}{2}, -\frac{1}{2} \)
You would enter these values separated by a comma.
\[
b^2 = \frac{10}{40}
\]
This simplifies to:
\[
b^2 = \frac{1}{4}
\]
Next, we take the square root of both sides. Remember that taking the square root of both sides gives us both the positive and negative square roots:
\[
b = \pm \sqrt{\frac{1}{4}}
\]
Calculating the square root, we have:
\[
b = \pm \frac{1}{2}
\]
Thus, the solutions for \( b \) are:
\[
b = \frac{1}{2}, -\frac{1}{2}
\]
So, the correct choice is:
**A.** \( b = \frac{1}{2}, -\frac{1}{2} \)
You would enter these values separated by a comma.