x^2-31.5x+12.875=0

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Solution for x^2-31.5x+12.875=0 equation: 


Simplifying
x2 + -31.5x + 12.875 = 0

Reorder the terms:
12.875 + -31.5x + x2 = 0

Solving
12.875 + -31.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12.875' to each side of the equation.
12.875 + -31.5x + -12.875 + x2 = 0 + -12.875

Reorder the terms:
12.875 + -12.875 + -31.5x + x2 = 0 + -12.875

Combine like terms: 12.875 + -12.875 = 0.000
0.000 + -31.5x + x2 = 0 + -12.875
-31.5x + x2 = 0 + -12.875

Combine like terms: 0 + -12.875 = -12.875
-31.5x + x2 = -12.875

The x term is -31.5x.  Take half its coefficient (-15.75).
Square it (248.0625) and add it to both sides.

Add '248.0625' to each side of the equation.
-31.5x + 248.0625 + x2 = -12.875 + 248.0625

Reorder the terms:
248.0625 + -31.5x + x2 = -12.875 + 248.0625

Combine like terms: -12.875 + 248.0625 = 235.1875
248.0625 + -31.5x + x2 = 235.1875

Factor a perfect square on the left side:
(x + -15.75)(x + -15.75) = 235.1875

Calculate the square root of the right side: 15.335824073

Break this problem into two subproblems by setting 
(x + -15.75) equal to 15.335824073 and -15.335824073.


Subproblem 1
x + -15.75 = 15.335824073

Simplifying
x + -15.75 = 15.335824073

Reorder the terms:
-15.75 + x = 15.335824073

Solving
-15.75 + x = 15.335824073

Solving for variable 'x'.

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

Add '15.75' to each side of the equation.
-15.75 + 15.75 + x = 15.335824073 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + x = 15.335824073 + 15.75
x = 15.335824073 + 15.75

Combine like terms: 15.335824073 + 15.75 = 31.085824073
x = 31.085824073

Simplifying
x = 31.085824073


Subproblem 2
x + -15.75 = -15.335824073

Simplifying
x + -15.75 = -15.335824073

Reorder the terms:
-15.75 + x = -15.335824073

Solving
-15.75 + x = -15.335824073

Solving for variable 'x'.

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

Add '15.75' to each side of the equation.
-15.75 + 15.75 + x = -15.335824073 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + x = -15.335824073 + 15.75
x = -15.335824073 + 15.75

Combine like terms: -15.335824073 + 15.75 = 0.414175927
x = 0.414175927

Simplifying
x = 0.414175927


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.085824073, 0.414175927}

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