x^2-16x+64=12

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Solution for x^2-16x+64=12 equation: 


Simplifying
x2 + -16x + 64 = 12

Reorder the terms:
64 + -16x + x2 = 12

Solving
64 + -16x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
64 + -12 + -16x + x2 = 12 + -12

Combine like terms: 64 + -12 = 52
52 + -16x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
52 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + -16x + -52 + x2 = 0 + -52

Reorder the terms:
52 + -52 + -16x + x2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -16x + x2 = 0 + -52
-16x + x2 = 0 + -52

Combine like terms: 0 + -52 = -52
-16x + x2 = -52

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 = -52 + 64

Reorder the terms:
64 + -16x + x2 = -52 + 64

Combine like terms: -52 + 64 = 12
64 + -16x + x2 = 12

Factor a perfect square on the left side:
(x + -8)(x + -8) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -8) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + -8 = 3.464101615

Simplifying
x + -8 = 3.464101615

Reorder the terms:
-8 + x = 3.464101615

Solving
-8 + x = 3.464101615

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 = 3.464101615 + 8

Combine like terms: -8 + 8 = 0
0 + x = 3.464101615 + 8
x = 3.464101615 + 8

Combine like terms: 3.464101615 + 8 = 11.464101615
x = 11.464101615

Simplifying
x = 11.464101615


Subproblem 2
x + -8 = -3.464101615

Simplifying
x + -8 = -3.464101615

Reorder the terms:
-8 + x = -3.464101615

Solving
-8 + x = -3.464101615

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 = -3.464101615 + 8

Combine like terms: -8 + 8 = 0
0 + x = -3.464101615 + 8
x = -3.464101615 + 8

Combine like terms: -3.464101615 + 8 = 4.535898385
x = 4.535898385

Simplifying
x = 4.535898385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.464101615, 4.535898385}

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