To solve the equation \( x^2 = 20 \), we need to isolate \( x \) by taking the square root of both sides. Here is the step-by-step process:
1. Start with the given equation:
[tex]\[
x^2 = 20
\][/tex]
2. Take the square root of both sides to solve for \( x \):
[tex]\[
x = \pm \sqrt{20}
\][/tex]
3. Simplify \(\sqrt{20}\). The number 20 can be factored into its prime factors:
[tex]\[
20 = 4 \times 5
\][/tex]
4. Therefore, we can write:
[tex]\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2 \sqrt{5}
\][/tex]
5. Substitute back into the equation:
[tex]\[
x = \pm 2 \sqrt{5}
\][/tex]
Thus, the solutions to the equation \( x^2 = 20 \) are:
[tex]\[
x = \pm 2 \sqrt{5}
\][/tex]
Therefore, the correct answer from the given choices is
D. [tex]\( x = \pm 2 \sqrt{5} \)[/tex]
