To determine the roots of the equation \(7^2 + 2x - 8 = 0\) by factorization, let's follow a step-by-step approach.
1. Expand and Simplify
The given equation is
[tex]\[
7^2 + 2x - 8 = 0
\][/tex]
First, calculate \(7^2\):
[tex]\[
7^2 = 49
\][/tex]
So the equation simplifies to:
[tex]\[
49 + 2x - 8 = 0
\][/tex]
2. Combine Like Terms
Simplify the constants:
[tex]\[
49 - 8 = 41
\][/tex]
Thus, the equation transforms into:
[tex]\[
41 + 2x = 0
\][/tex]
3. Rearrange the Equation
Move the constant term to the other side of the equation to isolate the term with \(x\):
[tex]\[
2x = -41
\][/tex]
4. Solve for \(x\)
Divide both sides of the equation by 2 to solve for \(x\):
[tex]\[
x = \frac{-41}{2}
\][/tex]
Therefore, the root of the equation \(7^2 + 2x - 8 = 0\) is:
[tex]\[
x = -\frac{41}{2}
\][/tex]
