Question

8x2−3=2



Responses

x=±10√4
x equals plus or minus fraction numerator square root of 10 end root end numerator over denominator 4

x=±10√2
x equals plus or minus fraction numerator square root of 10 end root end numerator over denominator 2

x=±5√2
x equals plus or minus fraction numerator square root of 5 end root end numerator over denominator 2

x=±5√4

Answer 1

To solve the equation \( 8x^2 - 3 = 2 \), we can follow these steps:

1. First, move the constant on the right side:
\[
8x^2 - 3 - 2 = 0 \quad \Rightarrow \quad 8x^2 - 5 = 0
\]

2. Next, add 5 to both sides:
\[
8x^2 = 5
\]

3. Now, divide both sides by 8:
\[
x^2 = \frac{5}{8}
\]

4. Take the square root of both sides:
\[
x = \pm \sqrt{\frac{5}{8}} = \pm \sqrt{\frac{5}{4 \times 2}} = \pm \sqrt{\frac{5}{4}} \cdot \frac{1}{\sqrt{2}} = \pm \frac{\sqrt{5}}{2\sqrt{2}} = \pm \frac{\sqrt{5}}{2} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \pm \frac{\sqrt{10}}{4}
\]

So, the correct answer is:
\[
x = \pm \frac{\sqrt{10}}{4}
\]

Among the given responses:
- \( x = \pm \frac{\sqrt{10}}{4} \) is the correct solution.

None of the other responses fit.