x^2-12.5x+13.5=0

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Solution for x^2-12.5x+13.5=0 equation: 


Simplifying
x2 + -12.5x + 13.5 = 0

Reorder the terms:
13.5 + -12.5x + x2 = 0

Solving
13.5 + -12.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -12.5x + -13.5 + x2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -12.5x + x2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -12.5x + x2 = 0 + -13.5
-12.5x + x2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-12.5x + x2 = -13.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -13.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -13.5 + 39.0625

Combine like terms: -13.5 + 39.0625 = 25.5625
39.0625 + -12.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + -6.25) equal to 5.055937104 and -5.055937104.


Subproblem 1
x + -6.25 = 5.055937104

Simplifying
x + -6.25 = 5.055937104

Reorder the terms:
-6.25 + x = 5.055937104

Solving
-6.25 + x = 5.055937104

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 5.055937104 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 5.055937104 + 6.25
x = 5.055937104 + 6.25

Combine like terms: 5.055937104 + 6.25 = 11.305937104
x = 11.305937104

Simplifying
x = 11.305937104


Subproblem 2
x + -6.25 = -5.055937104

Simplifying
x + -6.25 = -5.055937104

Reorder the terms:
-6.25 + x = -5.055937104

Solving
-6.25 + x = -5.055937104

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -5.055937104 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -5.055937104 + 6.25
x = -5.055937104 + 6.25

Combine like terms: -5.055937104 + 6.25 = 1.194062896
x = 1.194062896

Simplifying
x = 1.194062896


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.305937104, 1.194062896}

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