Question

Solve the quadratic equation 1/2x^2-4=0

Answer 1

To solve the quadratic equation \(\frac{1}{2}x^2 - 4 = 0\), we can start by isolating the \(x^2\) term.

1. Add 4 to both sides:
\[
\frac{1}{2}x^2 = 4
\]

2. Multiply both sides by 2 to eliminate the fraction:
\[
x^2 = 8
\]

3. Now, take the square root of both sides:
\[
x = \pm \sqrt{8}
\]

4. Simplify \(\sqrt{8}\):
\[
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]

5. Thus, the solutions are:
\[
x = 2\sqrt{2} \quad \text{and} \quad x = -2\sqrt{2}
\]

So, the solutions to the equation \(\frac{1}{2}x^2 - 4 = 0\) are:
\[
x = 2\sqrt{2} \quad \text{and} \quad x = -2\sqrt{2}
\]