To solve the quadratic equation [tex]\(x^2 - 16 = 0\)[/tex], we need to find the values of [tex]\(x\)[/tex] that satisfy this equation. Let's work through the problem step by step.
1. Start with the given quadratic equation:
[tex]\[ x^2 - 16 = 0 \][/tex]
2. Rearrange the equation to isolate [tex]\(x^2\)[/tex]:
[tex]\[ x^2 = 16 \][/tex]
3. Solve for [tex]\(x\)[/tex] by taking the square root of both sides:
[tex]\[ x = \pm \sqrt{16} \][/tex]
4. Simplify the square root:
[tex]\[ \sqrt{16} = 4 \][/tex]
5. Then, we have two solutions:
[tex]\[ x = 4 \quad \text{and} \quad x = -4 \][/tex]
So, the solutions to the quadratic equation [tex]\(x^2 - 16 = 0\)[/tex] are:
[tex]\[ x = 4 \][/tex] and [tex]\[ x = -4 \][/tex]
Therefore, the correct answer is:
[tex]\[ x = 4 \quad \text{and} \quad x = -4 \][/tex]
