To solve the equation [tex]\(x^2 - 4 = 0\)[/tex], follow these steps:
1. Isolate the term involving [tex]\(x\)[/tex]: Add 4 to both sides of the equation to get rid of the constant term on the left side.
[tex]\[
x^2 - 4 + 4 = 0 + 4
\][/tex]
Simplifies to:
[tex]\[
x^2 = 4
\][/tex]
2. Solve for [tex]\(x\)[/tex]: To find the value of [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember that taking the square root of a number gives two solutions, one positive and one negative.
[tex]\[
x = \pm\sqrt{4}
\][/tex]
3. Simplify the square root: The square root of 4 is 2.
[tex]\[
x = \pm 2
\][/tex]
Therefore, the solutions to the equation [tex]\(x^2 - 4 = 0\)[/tex] are:
[tex]\[
x = 2 \quad \text{or} \quad x = -2
\][/tex]
Given the choices:
- [tex]\(x = -4\)[/tex] or [tex]\(x = 4\)[/tex]
- [tex]\(x = -2\)[/tex] or [tex]\(x = 2\)[/tex]
- [tex]\(x = 2\)[/tex]
- [tex]\(x = 4\)[/tex]
The correct solution is [tex]\(x = -2\)[/tex] or [tex]\(x = 2\)[/tex].
