x^2-12x+36=4x+4

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Solution for x^2-12x+36=4x+4 equation:


Simplifying
x2 + -12x + 36 = 4x + 4

Reorder the terms:
36 + -12x + x2 = 4x + 4

Reorder the terms:
36 + -12x + x2 = 4 + 4x

Solving
36 + -12x + x2 = 4 + 4x

Solving for variable 'x'.

Reorder the terms:
36 + -4 + -12x + -4x + x2 = 4 + 4x + -4 + -4x

Combine like terms: 36 + -4 = 32
32 + -12x + -4x + x2 = 4 + 4x + -4 + -4x

Combine like terms: -12x + -4x = -16x
32 + -16x + x2 = 4 + 4x + -4 + -4x

Reorder the terms:
32 + -16x + x2 = 4 + -4 + 4x + -4x

Combine like terms: 4 + -4 = 0
32 + -16x + x2 = 0 + 4x + -4x
32 + -16x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
32 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -16x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -16x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -16x + x2 = 0 + -32
-16x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-16x + x2 = -32

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 = -32 + 64

Reorder the terms:
64 + -16x + x2 = -32 + 64

Combine like terms: -32 + 64 = 32
64 + -16x + x2 = 32

Factor a perfect square on the left side:
(x + -8)(x + -8) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + -8) equal to 5.656854249 and -5.656854249.

Subproblem 1

x + -8 = 5.656854249 Simplifying x + -8 = 5.656854249 Reorder the terms: -8 + x = 5.656854249 Solving -8 + x = 5.656854249 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 = 5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x = 5.656854249 + 8 x = 5.656854249 + 8 Combine like terms: 5.656854249 + 8 = 13.656854249 x = 13.656854249 Simplifying x = 13.656854249

Subproblem 2

x + -8 = -5.656854249 Simplifying x + -8 = -5.656854249 Reorder the terms: -8 + x = -5.656854249 Solving -8 + x = -5.656854249 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 = -5.656854249 + 8 Combine like terms: -8 + 8 = 0 0 + x = -5.656854249 + 8 x = -5.656854249 + 8 Combine like terms: -5.656854249 + 8 = 2.343145751 x = 2.343145751 Simplifying x = 2.343145751

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.656854249, 2.343145751}

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