x^2-13x-12=0

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Solution for x^2-13x-12=0 equation: 


Simplifying
x2 + -13x + -12 = 0

Reorder the terms:
-12 + -13x + x2 = 0

Solving
-12 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -13x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -13x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -13x + x2 = 0 + 12
-13x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-13x + x2 = 12

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 12 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 12 + 42.25

Combine like terms: 12 + 42.25 = 54.25
42.25 + -13x + x2 = 54.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + -6.5) equal to 7.365459931 and -7.365459931.


Subproblem 1
x + -6.5 = 7.365459931

Simplifying
x + -6.5 = 7.365459931

Reorder the terms:
-6.5 + x = 7.365459931

Solving
-6.5 + x = 7.365459931

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 7.365459931 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 7.365459931 + 6.5
x = 7.365459931 + 6.5

Combine like terms: 7.365459931 + 6.5 = 13.865459931
x = 13.865459931

Simplifying
x = 13.865459931


Subproblem 2
x + -6.5 = -7.365459931

Simplifying
x + -6.5 = -7.365459931

Reorder the terms:
-6.5 + x = -7.365459931

Solving
-6.5 + x = -7.365459931

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -7.365459931 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -7.365459931 + 6.5
x = -7.365459931 + 6.5

Combine like terms: -7.365459931 + 6.5 = -0.865459931
x = -0.865459931

Simplifying
x = -0.865459931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.865459931, -0.865459931}

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