4x+22=x^2-118

Solution for 4x+22=x^2-118 equation:

Simplifying
4x + 22 = x2 + -118

Reorder the terms:
22 + 4x = x2 + -118

Reorder the terms:
22 + 4x = -118 + x2

Solving
22 + 4x = -118 + x2

Solving for variable 'x'.

Reorder the terms:
22 + 118 + 4x + -1x2 = -118 + x2 + 118 + -1x2

Combine like terms: 22 + 118 = 140
140 + 4x + -1x2 = -118 + x2 + 118 + -1x2

Reorder the terms:
140 + 4x + -1x2 = -118 + 118 + x2 + -1x2

Combine like terms: -118 + 118 = 0
140 + 4x + -1x2 = 0 + x2 + -1x2
140 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
140 + 4x + -1x2 = 0

Factor a trinomial.
(14 + -1x)(10 + x) = 0

Subproblem 1
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {14, -10}