x^2-15x+56.25=8

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Solution for x^2-15x+56.25=8 equation: 


Simplifying
x2 + -15x + 56.25 = 8

Reorder the terms:
56.25 + -15x + x2 = 8

Solving
56.25 + -15x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
56.25 + -8 + -15x + x2 = 8 + -8

Combine like terms: 56.25 + -8 = 48.25
48.25 + -15x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
48.25 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-48.25' to each side of the equation.
48.25 + -15x + -48.25 + x2 = 0 + -48.25

Reorder the terms:
48.25 + -48.25 + -15x + x2 = 0 + -48.25

Combine like terms: 48.25 + -48.25 = 0.00
0.00 + -15x + x2 = 0 + -48.25
-15x + x2 = 0 + -48.25

Combine like terms: 0 + -48.25 = -48.25
-15x + x2 = -48.25

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 = -48.25 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -48.25 + 56.25

Combine like terms: -48.25 + 56.25 = 8
56.25 + -15x + x2 = 8

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -7.5) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -7.5 = 2.828427125

Simplifying
x + -7.5 = 2.828427125

Reorder the terms:
-7.5 + x = 2.828427125

Solving
-7.5 + x = 2.828427125

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 = 2.828427125 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 2.828427125 + 7.5
x = 2.828427125 + 7.5

Combine like terms: 2.828427125 + 7.5 = 10.328427125
x = 10.328427125

Simplifying
x = 10.328427125


Subproblem 2
x + -7.5 = -2.828427125

Simplifying
x + -7.5 = -2.828427125

Reorder the terms:
-7.5 + x = -2.828427125

Solving
-7.5 + x = -2.828427125

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 = -2.828427125 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -2.828427125 + 7.5
x = -2.828427125 + 7.5

Combine like terms: -2.828427125 + 7.5 = 4.671572875
x = 4.671572875

Simplifying
x = 4.671572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.328427125, 4.671572875}

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