Certainly! Let's solve the equation [tex]\( x^2 - 15 = 34 \)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
x^2 - 15 = 34
\][/tex]
2. Isolate the [tex]\( x^2 \)[/tex] term by adding 15 to both sides of the equation:
[tex]\[
x^2 = 34 + 15
\][/tex]
3. Simplify the right side of the equation:
[tex]\[
x^2 = 49
\][/tex]
4. To solve for [tex]\( x \)[/tex], we take the square root of both sides. Remember that taking the square root yields two solutions, one positive and one negative:
[tex]\[
x = \pm \sqrt{49}
\][/tex]
5. Simplify the square root:
[tex]\[
x = \pm 7
\][/tex]
So, the solutions to the equation [tex]\( x^2 - 15 = 34 \)[/tex] are:
[tex]\[
x = -7 \quad \text{and} \quad x = 7
\][/tex]
