x^2-16x-64=-80

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Solution for x^2-16x-64=-80 equation: 


Simplifying
x2 + -16x + -64 = -80

Reorder the terms:
-64 + -16x + x2 = -80

Solving
-64 + -16x + x2 = -80

Solving for variable 'x'.

Reorder the terms:
-64 + 80 + -16x + x2 = -80 + 80

Combine like terms: -64 + 80 = 16
16 + -16x + x2 = -80 + 80

Combine like terms: -80 + 80 = 0
16 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -16x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -16x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -16x + x2 = 0 + -16
-16x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-16x + x2 = -16

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -16 + 64

Reorder the terms:
64 + -16x + x2 = -16 + 64

Combine like terms: -16 + 64 = 48
64 + -16x + x2 = 48

Factor a perfect square on the left side:
(x + -8)(x + -8) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + -8) equal to 6.92820323 and -6.92820323.


Subproblem 1
x + -8 = 6.92820323

Simplifying
x + -8 = 6.92820323

Reorder the terms:
-8 + x = 6.92820323

Solving
-8 + x = 6.92820323

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 6.92820323 + 8

Combine like terms: -8 + 8 = 0
0 + x = 6.92820323 + 8
x = 6.92820323 + 8

Combine like terms: 6.92820323 + 8 = 14.92820323
x = 14.92820323

Simplifying
x = 14.92820323


Subproblem 2
x + -8 = -6.92820323

Simplifying
x + -8 = -6.92820323

Reorder the terms:
-8 + x = -6.92820323

Solving
-8 + x = -6.92820323

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -6.92820323 + 8

Combine like terms: -8 + 8 = 0
0 + x = -6.92820323 + 8
x = -6.92820323 + 8

Combine like terms: -6.92820323 + 8 = 1.07179677
x = 1.07179677

Simplifying
x = 1.07179677


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.92820323, 1.07179677}

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