To solve the equation [tex]\(x^2 + 4x - 2 = x^2 - x + 8\)[/tex], let's go through the process step-by-step:
1. Isolate one side of the equation:
First, we need to bring all the terms to one side of the equation to facilitate solving for [tex]\(x\)[/tex]. Let's move all terms to the left side by subtracting [tex]\( (x^2 - x + 8) \)[/tex] from both sides:
[tex]\[
(x^2 + 4x - 2) - (x^2 - x + 8) = 0
\][/tex]
2. Simplify the equation:
Distribute the subtraction through the parentheses:
[tex]\[
x^2 + 4x - 2 - x^2 + x - 8 = 0
\][/tex]
Combine like terms:
[tex]\[
(x^2 - x^2) + (4x + x) + (-2 - 8) = 0
\][/tex]
[tex]\[
0 + 5x - 10 = 0
\][/tex]
This simplifies to:
[tex]\[
5x - 10 = 0
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we will add 10 to both sides of the equation:
[tex]\[
5x - 10 + 10 = 0 + 10
\][/tex]
[tex]\[
5x = 10
\][/tex]
Now, divide both sides by 5:
[tex]\[
x = \frac{10}{5}
\][/tex]
[tex]\[
x = 2
\][/tex]
Thus, the solution to the equation [tex]\(x^2 + 4x - 2 = x^2 - x + 8\)[/tex] is:
[tex]\[
x = 2
\][/tex]
