Certainly! Let's solve the given mathematical equation step-by-step.
Given:
[tex]\[ x_2 = -8 + 17 \][/tex]
First, we need to evaluate the right-hand side:
[tex]\[ x_2 = -8 + 17 \][/tex]
[tex]\[ x_2 = 9 \][/tex]
Thus, we have:
[tex]\[ x^2 = 9 \][/tex]
Next, we need to solve for [tex]\( x \)[/tex]. The equation [tex]\( x^2 = 9 \)[/tex] implies that [tex]\( x \)[/tex] can be either the positive or the negative square root of 9. Therefore, we have two possible solutions:
[tex]\[ x = \sqrt{9} \][/tex]
[tex]\[ x = -\sqrt{9} \][/tex]
Evaluating the square roots, we get:
[tex]\[ \sqrt{9} = 3 \][/tex]
[tex]\[ -\sqrt{9} = -3 \][/tex]
Thus, the solutions to the equation [tex]\( x^2 = 9 \)[/tex] are:
[tex]\[ x = 3 \][/tex]
[tex]\[ x = -3 \][/tex]
So, the final solutions are:
[tex]\[ x_1 = 3 \][/tex]
[tex]\[ x_2 = -3 \][/tex]
Therefore, the values of [tex]\( x \)[/tex] are [tex]\( 3 \)[/tex] and [tex]\( -3 \)[/tex].
