x^2+22x+121=13

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Solution for x^2+22x+121=13 equation:


Simplifying
x2 + 22x + 121 = 13

Reorder the terms:
121 + 22x + x2 = 13

Solving
121 + 22x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
121 + -13 + 22x + x2 = 13 + -13

Combine like terms: 121 + -13 = 108
108 + 22x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
108 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-108' to each side of the equation.
108 + 22x + -108 + x2 = 0 + -108

Reorder the terms:
108 + -108 + 22x + x2 = 0 + -108

Combine like terms: 108 + -108 = 0
0 + 22x + x2 = 0 + -108
22x + x2 = 0 + -108

Combine like terms: 0 + -108 = -108
22x + x2 = -108

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -108 + 121

Reorder the terms:
121 + 22x + x2 = -108 + 121

Combine like terms: -108 + 121 = 13
121 + 22x + x2 = 13

Factor a perfect square on the left side:
(x + 11)(x + 11) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 11) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + 11 = 3.605551275 Simplifying x + 11 = 3.605551275 Reorder the terms: 11 + x = 3.605551275 Solving 11 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 3.605551275 + -11 Combine like terms: 11 + -11 = 0 0 + x = 3.605551275 + -11 x = 3.605551275 + -11 Combine like terms: 3.605551275 + -11 = -7.394448725 x = -7.394448725 Simplifying x = -7.394448725

Subproblem 2

x + 11 = -3.605551275 Simplifying x + 11 = -3.605551275 Reorder the terms: 11 + x = -3.605551275 Solving 11 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -3.605551275 + -11 Combine like terms: 11 + -11 = 0 0 + x = -3.605551275 + -11 x = -3.605551275 + -11 Combine like terms: -3.605551275 + -11 = -14.605551275 x = -14.605551275 Simplifying x = -14.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-7.394448725, -14.605551275}

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