Answer :
To solve the equation [tex]\(2x^2 + 65 = 227\)[/tex], we can follow these steps:
1. Subtract 65 from both sides:
[tex]\[
2x^2 + 65 - 65 = 227 - 65
\][/tex]
Simplifies to:
[tex]\[
2x^2 = 162
\][/tex]
2. Divide both sides by 2 to isolate [tex]\(x^2\)[/tex]:
[tex]\[
\frac{2x^2}{2} = \frac{162}{2}
\][/tex]
Simplifies to:
[tex]\[
x^2 = 81
\][/tex]
3. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \pm \sqrt{81}
\][/tex]
Evaluating the square root gives:
[tex]\[
x = \pm 9
\][/tex]
Therefore, the solutions to the equation [tex]\(2x^2 + 65 = 227\)[/tex] are [tex]\(x = 9\)[/tex] and [tex]\(x = -9\)[/tex].
1. Subtract 65 from both sides:
[tex]\[
2x^2 + 65 - 65 = 227 - 65
\][/tex]
Simplifies to:
[tex]\[
2x^2 = 162
\][/tex]
2. Divide both sides by 2 to isolate [tex]\(x^2\)[/tex]:
[tex]\[
\frac{2x^2}{2} = \frac{162}{2}
\][/tex]
Simplifies to:
[tex]\[
x^2 = 81
\][/tex]
3. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \pm \sqrt{81}
\][/tex]
Evaluating the square root gives:
[tex]\[
x = \pm 9
\][/tex]
Therefore, the solutions to the equation [tex]\(2x^2 + 65 = 227\)[/tex] are [tex]\(x = 9\)[/tex] and [tex]\(x = -9\)[/tex].
