Answer :
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]
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]
