x^2-17x-12=0

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Solution for x^2-17x-12=0 equation: 


Simplifying
x2 + -17x + -12 = 0

Reorder the terms:
-12 + -17x + x2 = 0

Solving
-12 + -17x + 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 + -17x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -17x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -17x + x2 = 0 + 12
-17x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-17x + x2 = 12

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = 12 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 12 + 72.25

Combine like terms: 12 + 72.25 = 84.25
72.25 + -17x + x2 = 84.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(x + -8.5) equal to 9.178779875 and -9.178779875.


Subproblem 1
x + -8.5 = 9.178779875

Simplifying
x + -8.5 = 9.178779875

Reorder the terms:
-8.5 + x = 9.178779875

Solving
-8.5 + x = 9.178779875

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 9.178779875 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 9.178779875 + 8.5
x = 9.178779875 + 8.5

Combine like terms: 9.178779875 + 8.5 = 17.678779875
x = 17.678779875

Simplifying
x = 17.678779875


Subproblem 2
x + -8.5 = -9.178779875

Simplifying
x + -8.5 = -9.178779875

Reorder the terms:
-8.5 + x = -9.178779875

Solving
-8.5 + x = -9.178779875

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -9.178779875 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -9.178779875 + 8.5
x = -9.178779875 + 8.5

Combine like terms: -9.178779875 + 8.5 = -0.678779875
x = -0.678779875

Simplifying
x = -0.678779875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.678779875, -0.678779875}

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