-5x^2+128x-12=0

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Solution for -5x^2+128x-12=0 equation: 


Simplifying
-5x2 + 128x + -12 = 0

Reorder the terms:
-12 + 128x + -5x2 = 0

Solving
-12 + 128x + -5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
2.4 + -25.6x + x2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -25.6x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -25.6x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -25.6x + x2 = 0 + -2.4
-25.6x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-25.6x + x2 = -2.4

The x term is -25.6x.  Take half its coefficient (-12.8).
Square it (163.84) and add it to both sides.

Add '163.84' to each side of the equation.
-25.6x + 163.84 + x2 = -2.4 + 163.84

Reorder the terms:
163.84 + -25.6x + x2 = -2.4 + 163.84

Combine like terms: -2.4 + 163.84 = 161.44
163.84 + -25.6x + x2 = 161.44

Factor a perfect square on the left side:
(x + -12.8)(x + -12.8) = 161.44

Calculate the square root of the right side: 12.705904139

Break this problem into two subproblems by setting 
(x + -12.8) equal to 12.705904139 and -12.705904139.


Subproblem 1
x + -12.8 = 12.705904139

Simplifying
x + -12.8 = 12.705904139

Reorder the terms:
-12.8 + x = 12.705904139

Solving
-12.8 + x = 12.705904139

Solving for variable 'x'.

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

Add '12.8' to each side of the equation.
-12.8 + 12.8 + x = 12.705904139 + 12.8

Combine like terms: -12.8 + 12.8 = 0.0
0.0 + x = 12.705904139 + 12.8
x = 12.705904139 + 12.8

Combine like terms: 12.705904139 + 12.8 = 25.505904139
x = 25.505904139

Simplifying
x = 25.505904139


Subproblem 2
x + -12.8 = -12.705904139

Simplifying
x + -12.8 = -12.705904139

Reorder the terms:
-12.8 + x = -12.705904139

Solving
-12.8 + x = -12.705904139

Solving for variable 'x'.

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

Add '12.8' to each side of the equation.
-12.8 + 12.8 + x = -12.705904139 + 12.8

Combine like terms: -12.8 + 12.8 = 0.0
0.0 + x = -12.705904139 + 12.8
x = -12.705904139 + 12.8

Combine like terms: -12.705904139 + 12.8 = 0.094095861
x = 0.094095861

Simplifying
x = 0.094095861


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.505904139, 0.094095861}

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