0.8x^2-28x+122.5=0

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Solution for 0.8x^2-28x+122.5=0 equation: 


Simplifying
0.8x2 + -28x + 122.5 = 0

Reorder the terms:
122.5 + -28x + 0.8x2 = 0

Solving
122.5 + -28x + 0.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.8'.
153.125 + -35x + x2 = 0

Move the constant term to the right:

Add '-153.125' to each side of the equation.
153.125 + -35x + -153.125 + x2 = 0 + -153.125

Reorder the terms:
153.125 + -153.125 + -35x + x2 = 0 + -153.125

Combine like terms: 153.125 + -153.125 = 0.000
0.000 + -35x + x2 = 0 + -153.125
-35x + x2 = 0 + -153.125

Combine like terms: 0 + -153.125 = -153.125
-35x + x2 = -153.125

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -153.125 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -153.125 + 306.25

Combine like terms: -153.125 + 306.25 = 153.125
306.25 + -35x + x2 = 153.125

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 153.125

Calculate the square root of the right side: 12.374368671

Break this problem into two subproblems by setting 
(x + -17.5) equal to 12.374368671 and -12.374368671.


Subproblem 1
x + -17.5 = 12.374368671

Simplifying
x + -17.5 = 12.374368671

Reorder the terms:
-17.5 + x = 12.374368671

Solving
-17.5 + x = 12.374368671

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 12.374368671 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 12.374368671 + 17.5
x = 12.374368671 + 17.5

Combine like terms: 12.374368671 + 17.5 = 29.874368671
x = 29.874368671

Simplifying
x = 29.874368671


Subproblem 2
x + -17.5 = -12.374368671

Simplifying
x + -17.5 = -12.374368671

Reorder the terms:
-17.5 + x = -12.374368671

Solving
-17.5 + x = -12.374368671

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -12.374368671 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -12.374368671 + 17.5
x = -12.374368671 + 17.5

Combine like terms: -12.374368671 + 17.5 = 5.125631329
x = 5.125631329

Simplifying
x = 5.125631329


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.874368671, 5.125631329}

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