To find the solutions of the equation [tex]\( x^2 + 15 = 79 \)[/tex], we will go through the following steps:
1. Rewrite the Equation:
The given equation is [tex]\( x^2 + 15 = 79 \)[/tex]. We need to isolate [tex]\( x^2 \)[/tex], so we subtract 15 from both sides of the equation:
[tex]\[
x^2 = 79 - 15
\][/tex]
2. Simplify:
Calculate [tex]\( 79 - 15 \)[/tex]:
[tex]\[
x^2 = 64
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], take the square root of both sides of the equation. Remember that taking the square root of a number could yield both positive and negative results:
[tex]\[
x = \pm \sqrt{64}
\][/tex]
Since the square root of 64 is 8, we get:
[tex]\[
x = \pm 8
\][/tex]
Thus, [tex]\( x \)[/tex] could be either [tex]\( 8 \)[/tex] or [tex]\( -8 \)[/tex].
Given the solutions [tex]\( 8 \)[/tex] and [tex]\( -8 \)[/tex], we need to check which options apply:
- [tex]\( -\sqrt{94} \)[/tex]: Not correct.
- [tex]\( -\sqrt{15} - \sqrt{79} \)[/tex]: Not correct.
- [tex]\( 8 \)[/tex]: Correct.
- [tex]\( \sqrt{94} \)[/tex]: Not correct.
- [tex]\( -8 \)[/tex]: Correct.
- [tex]\( -\sqrt{15} + \sqrt{79} \)[/tex]: Not correct.
Therefore, the correct solutions for the equation [tex]\( x^2 + 15 = 79 \)[/tex] are:
- [tex]\( 8 \)[/tex]
- [tex]\( -8 \)[/tex]
