x^2-8x-31=0

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Solution for x^2-8x-31=0 equation: 


Simplifying
x2 + -8x + -31 = 0

Reorder the terms:
-31 + -8x + x2 = 0

Solving
-31 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -8x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -8x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -8x + x2 = 0 + 31
-8x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-8x + x2 = 31

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 31 + 16

Reorder the terms:
16 + -8x + x2 = 31 + 16

Combine like terms: 31 + 16 = 47
16 + -8x + x2 = 47

Factor a perfect square on the left side:
(x + -4)(x + -4) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + -4) equal to 6.8556546 and -6.8556546.


Subproblem 1
x + -4 = 6.8556546

Simplifying
x + -4 = 6.8556546

Reorder the terms:
-4 + x = 6.8556546

Solving
-4 + x = 6.8556546

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 6.8556546 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.8556546 + 4
x = 6.8556546 + 4

Combine like terms: 6.8556546 + 4 = 10.8556546
x = 10.8556546

Simplifying
x = 10.8556546


Subproblem 2
x + -4 = -6.8556546

Simplifying
x + -4 = -6.8556546

Reorder the terms:
-4 + x = -6.8556546

Solving
-4 + x = -6.8556546

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -6.8556546 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.8556546 + 4
x = -6.8556546 + 4

Combine like terms: -6.8556546 + 4 = -2.8556546
x = -2.8556546

Simplifying
x = -2.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.8556546, -2.8556546}

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