To solve the quadratic equation [tex]\(2x^2 - 9 = 121\)[/tex] by taking square roots, follow these step-by-step instructions:
1. Isolate the quadratic term:
[tex]\[
2x^2 - 9 = 121
\][/tex]
Add 9 to both sides:
[tex]\[
2x^2 - 9 + 9 = 121 + 9
\][/tex]
Simplifying, we get:
[tex]\[
2x^2 = 130
\][/tex]
2. Solve for [tex]\(x^2\)[/tex]:
Divide both sides by 2:
[tex]\[
x^2 = \frac{130}{2}
\][/tex]
Simplifying, we have:
[tex]\[
x^2 = 65
\][/tex]
3. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \pm \sqrt{65}
\][/tex]
4. Calculate the numerical values:
Find the square root of 65 and round to the nearest tenth:
[tex]\[
\sqrt{65} \approx 8.1
\][/tex]
So, the two solutions for [tex]\(x\)[/tex] are:
[tex]\[
x = 8.1 \quad \text{and} \quad x = -8.1
\][/tex]
Therefore, the answer in the required format, with no spaces, is:
[tex]\[
x = 8.1,-8.1
\][/tex]
