x=64+16x+x^2-144

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Solution for x=64+16x+x^2-144 equation:


Simplifying
x = 64 + 16x + x2 + -144

Reorder the terms:
x = 64 + -144 + 16x + x2

Combine like terms: 64 + -144 = -80
x = -80 + 16x + x2

Solving
x = -80 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
80 + x + -16x + -1x2 = -80 + 16x + x2 + 80 + -16x + -1x2

Combine like terms: x + -16x = -15x
80 + -15x + -1x2 = -80 + 16x + x2 + 80 + -16x + -1x2

Reorder the terms:
80 + -15x + -1x2 = -80 + 80 + 16x + -16x + x2 + -1x2

Combine like terms: -80 + 80 = 0
80 + -15x + -1x2 = 0 + 16x + -16x + x2 + -1x2
80 + -15x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
80 + -15x + -1x2 = 0 + x2 + -1x2
80 + -15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + -15x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-80 + 15x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 15x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 15x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 15x + x2 = 0 + 80
15x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
15x + x2 = 80

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 80 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 80 + 56.25

Combine like terms: 80 + 56.25 = 136.25
56.25 + 15x + x2 = 136.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 136.25

Calculate the square root of the right side: 11.67261753

Break this problem into two subproblems by setting 
(x + 7.5) equal to 11.67261753 and -11.67261753.

Subproblem 1

x + 7.5 = 11.67261753 Simplifying x + 7.5 = 11.67261753 Reorder the terms: 7.5 + x = 11.67261753 Solving 7.5 + x = 11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 11.67261753 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 11.67261753 + -7.5 x = 11.67261753 + -7.5 Combine like terms: 11.67261753 + -7.5 = 4.17261753 x = 4.17261753 Simplifying x = 4.17261753

Subproblem 2

x + 7.5 = -11.67261753 Simplifying x + 7.5 = -11.67261753 Reorder the terms: 7.5 + x = -11.67261753 Solving 7.5 + x = -11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -11.67261753 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -11.67261753 + -7.5 x = -11.67261753 + -7.5 Combine like terms: -11.67261753 + -7.5 = -19.17261753 x = -19.17261753 Simplifying x = -19.17261753

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.17261753, -19.17261753}

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