-1.25*x^2=-11x+17

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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 = 5.76
19.36 + -8.8x + x2 = 5.76

Factor a perfect square on the left side:
(x + -4.4)(x + -4.4) = 5.76

Calculate the square root of the right side: 2.4

Break this problem into two subproblems by setting 
(x + -4.4) equal to 2.4 and -2.4.


Subproblem 1
x + -4.4 = 2.4

Simplifying
x + -4.4 = 2.4

Reorder the terms:
-4.4 + x = 2.4

Solving
-4.4 + x = 2.4

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 = 2.4 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + x = 2.4 + 4.4
x = 2.4 + 4.4

Combine like terms: 2.4 + 4.4 = 6.8
x = 6.8

Simplifying
x = 6.8


Subproblem 2
x + -4.4 = -2.4

Simplifying
x + -4.4 = -2.4

Reorder the terms:
-4.4 + x = -2.4

Solving
-4.4 + x = -2.4

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 = -2.4 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + x = -2.4 + 4.4
x = -2.4 + 4.4

Combine like terms: -2.4 + 4.4 = 2
x = 2

Simplifying
x = 2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.8, 2}

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