x(x)+(x+1)(x+1)=113

Solution for x(x)+(x+1)(x+1)=113 equation:

Simplifying
x(x) + (x + 1)(x + 1) = 113

Multiply x * x
x2 + (x + 1)(x + 1) = 113

Reorder the terms:
x2 + (1 + x)(x + 1) = 113

Reorder the terms:
x2 + (1 + x)(1 + x) = 113

Multiply (1 + x) * (1 + x)
x2 + (1(1 + x) + x(1 + x)) = 113
x2 + ((1 * 1 + x * 1) + x(1 + x)) = 113
x2 + ((1 + 1x) + x(1 + x)) = 113
x2 + (1 + 1x + (1 * x + x * x)) = 113
x2 + (1 + 1x + (1x + x2)) = 113

Combine like terms: 1x + 1x = 2x
x2 + (1 + 2x + x2) = 113

Reorder the terms:
1 + 2x + x2 + x2 = 113

Combine like terms: x2 + x2 = 2x2
1 + 2x + 2x2 = 113

Solving
1 + 2x + 2x2 = 113

Solving for variable 'x'.

Reorder the terms:
1 + -113 + 2x + 2x2 = 113 + -113

Combine like terms: 1 + -113 = -112
-112 + 2x + 2x2 = 113 + -113

Combine like terms: 113 + -113 = 0
-112 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(7 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-8, 7}