x^2-8x-93=0

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Solution for x^2-8x-93=0 equation: 


Simplifying
x2 + -8x + -93 = 0

Reorder the terms:
-93 + -8x + x2 = 0

Solving
-93 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + -8x + 93 + x2 = 0 + 93

Reorder the terms:
-93 + 93 + -8x + x2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + -8x + x2 = 0 + 93
-8x + x2 = 0 + 93

Combine like terms: 0 + 93 = 93
-8x + x2 = 93

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 = 93 + 16

Reorder the terms:
16 + -8x + x2 = 93 + 16

Combine like terms: 93 + 16 = 109
16 + -8x + x2 = 109

Factor a perfect square on the left side:
(x + -4)(x + -4) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(x + -4) equal to 10.440306509 and -10.440306509.


Subproblem 1
x + -4 = 10.440306509

Simplifying
x + -4 = 10.440306509

Reorder the terms:
-4 + x = 10.440306509

Solving
-4 + x = 10.440306509

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 = 10.440306509 + 4

Combine like terms: -4 + 4 = 0
0 + x = 10.440306509 + 4
x = 10.440306509 + 4

Combine like terms: 10.440306509 + 4 = 14.440306509
x = 14.440306509

Simplifying
x = 14.440306509


Subproblem 2
x + -4 = -10.440306509

Simplifying
x + -4 = -10.440306509

Reorder the terms:
-4 + x = -10.440306509

Solving
-4 + x = -10.440306509

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 = -10.440306509 + 4

Combine like terms: -4 + 4 = 0
0 + x = -10.440306509 + 4
x = -10.440306509 + 4

Combine like terms: -10.440306509 + 4 = -6.440306509
x = -6.440306509

Simplifying
x = -6.440306509


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.440306509, -6.440306509}

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