0=1.25x^2-15x+25

Solution for 0=1.25x^2-15x+25 equation:

Simplifying
0 = 1.25x2 + -15x + 25

Reorder the terms:
0 = 25 + -15x + 1.25x2

Solving
0 = 25 + -15x + 1.25x2

Solving for variable 'x'.

Combine like terms: 0 + -25 = -25
-25 + 15x + -1.25x2 = 25 + -15x + 1.25x2 + -25 + 15x + -1.25x2

Reorder the terms:
-25 + 15x + -1.25x2 = 25 + -25 + -15x + 15x + 1.25x2 + -1.25x2

Combine like terms: 25 + -25 = 0
-25 + 15x + -1.25x2 = 0 + -15x + 15x + 1.25x2 + -1.25x2
-25 + 15x + -1.25x2 = -15x + 15x + 1.25x2 + -1.25x2

Combine like terms: -15x + 15x = 0
-25 + 15x + -1.25x2 = 0 + 1.25x2 + -1.25x2
-25 + 15x + -1.25x2 = 1.25x2 + -1.25x2

Combine like terms: 1.25x2 + -1.25x2 = 0.00
-25 + 15x + -1.25x2 = 0.00

Begin completing the square.  Divide all terms by
-1.25 the coefficient of the squared term: 

Divide each side by '-1.25'.
20 + -12x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -12x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -12x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -12x + x2 = 0 + -20
-12x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-12x + x2 = -20

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -20 + 36

Reorder the terms:
36 + -12x + x2 = -20 + 36

Combine like terms: -20 + 36 = 16
36 + -12x + x2 = 16

Factor a perfect square on the left side:
(x + -6)(x + -6) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + -6) equal to 4 and -4.

Subproblem 1
x + -6 = 4

Simplifying
x + -6 = 4

Reorder the terms:
-6 + x = 4

Solving
-6 + x = 4

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 4 + 6

Combine like terms: -6 + 6 = 0
0 + x = 4 + 6
x = 4 + 6

Combine like terms: 4 + 6 = 10
x = 10

Simplifying
x = 10

Subproblem 2
x + -6 = -4

Simplifying
x + -6 = -4

Reorder the terms:
-6 + x = -4

Solving
-6 + x = -4

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -4 + 6

Combine like terms: -6 + 6 = 0
0 + x = -4 + 6
x = -4 + 6

Combine like terms: -4 + 6 = 2
x = 2

Simplifying
x = 2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, 2}