1.25*x^2=-11x+17

Solution for 1.25*x^2=-11x+17 equation:

Simplifying
1.25x2 = -11x + 17

Reorder the terms:
1.25x2 = 17 + -11x

Solving
1.25x2 = 17 + -11x

Solving for variable 'x'.

Reorder the terms:
-17 + 11x + 1.25x2 = 17 + -11x + -17 + 11x

Reorder the terms:
-17 + 11x + 1.25x2 = 17 + -17 + -11x + 11x

Combine like terms: 17 + -17 = 0
-17 + 11x + 1.25x2 = 0 + -11x + 11x
-17 + 11x + 1.25x2 = -11x + 11x

Combine like terms: -11x + 11x = 0
-17 + 11x + 1.25x2 = 0

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

Divide each side by '1.25'.
-13.6 + 8.8x + x2 = 0

Move the constant term to the right:

Add '13.6' to each side of the equation.
-13.6 + 8.8x + 13.6 + x2 = 0 + 13.6

Reorder the terms:
-13.6 + 13.6 + 8.8x + x2 = 0 + 13.6

Combine like terms: -13.6 + 13.6 = 0.0
0.0 + 8.8x + x2 = 0 + 13.6
8.8x + x2 = 0 + 13.6

Combine like terms: 0 + 13.6 = 13.6
8.8x + x2 = 13.6

The x term is 8.8x.  Take half its coefficient (4.4).
Square it (19.36) and add it to both sides.

Add '19.36' to each side of the equation.
8.8x + 19.36 + x2 = 13.6 + 19.36

Reorder the terms:
19.36 + 8.8x + x2 = 13.6 + 19.36

Combine like terms: 13.6 + 19.36 = 32.96
19.36 + 8.8x + x2 = 32.96

Factor a perfect square on the left side:
(x + 4.4)(x + 4.4) = 32.96

Calculate the square root of the right side: 5.741080038

Break this problem into two subproblems by setting 
(x + 4.4) equal to 5.741080038 and -5.741080038.

Subproblem 1
x + 4.4 = 5.741080038

Simplifying
x + 4.4 = 5.741080038

Reorder the terms:
4.4 + x = 5.741080038

Solving
4.4 + x = 5.741080038

Solving for variable 'x'.

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

Add '-4.4' to each side of the equation.
4.4 + -4.4 + x = 5.741080038 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = 5.741080038 + -4.4
x = 5.741080038 + -4.4

Combine like terms: 5.741080038 + -4.4 = 1.341080038
x = 1.341080038

Simplifying
x = 1.341080038

Subproblem 2
x + 4.4 = -5.741080038

Simplifying
x + 4.4 = -5.741080038

Reorder the terms:
4.4 + x = -5.741080038

Solving
4.4 + x = -5.741080038

Solving for variable 'x'.

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

Add '-4.4' to each side of the equation.
4.4 + -4.4 + x = -5.741080038 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = -5.741080038 + -4.4
x = -5.741080038 + -4.4

Combine like terms: -5.741080038 + -4.4 = -10.141080038
x = -10.141080038

Simplifying
x = -10.141080038

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.341080038, -10.141080038}