Let's solve the equation step-by-step:
The given equation is:
[tex]\[ 4x^2 - 61 = 135 \][/tex]
1. Start by isolating the term involving [tex]\(x\)[/tex]. To do this, add 61 to both sides of the equation:
[tex]\[
4x^2 - 61 + 61 = 135 + 61
\][/tex]
[tex]\[
4x^2 = 196
\][/tex]
2. Next, divide both sides of the equation by 4 to solve for [tex]\(x^2\)[/tex]:
[tex]\[
\frac{4x^2}{4} = \frac{196}{4}
\][/tex]
[tex]\[
x^2 = 49
\][/tex]
3. To find [tex]\(x\)[/tex], take the square root of both sides:
[tex]\[
x = \pm \sqrt{49}
\][/tex]
[tex]\[
x = \pm 7
\][/tex]
Thus, the values of [tex]\(x\)[/tex] that satisfy the equation [tex]\(4x^2 - 61 = 135\)[/tex] are:
[tex]\[
x = -7 \quad \text{and} \quad x = 7
\][/tex]
So, the solutions to the equation are [tex]\(x = -7\)[/tex] and [tex]\(x = 7\)[/tex].
