0.2x^2+3.2x-5=0

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Solution for 0.2x^2+3.2x-5=0 equation: 


Simplifying
0.2x2 + 3.2x + -5 = 0

Reorder the terms:
-5 + 3.2x + 0.2x2 = 0

Solving
-5 + 3.2x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
-25 + 16x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 16x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 16x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 16x + x2 = 0 + 25
16x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
16x + x2 = 25

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 25 + 64

Reorder the terms:
64 + 16x + x2 = 25 + 64

Combine like terms: 25 + 64 = 89
64 + 16x + x2 = 89

Factor a perfect square on the left side:
(x + 8)(x + 8) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + 8) equal to 9.433981132 and -9.433981132.


Subproblem 1
x + 8 = 9.433981132

Simplifying
x + 8 = 9.433981132

Reorder the terms:
8 + x = 9.433981132

Solving
8 + x = 9.433981132

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 9.433981132 + -8

Combine like terms: 8 + -8 = 0
0 + x = 9.433981132 + -8
x = 9.433981132 + -8

Combine like terms: 9.433981132 + -8 = 1.433981132
x = 1.433981132

Simplifying
x = 1.433981132


Subproblem 2
x + 8 = -9.433981132

Simplifying
x + 8 = -9.433981132

Reorder the terms:
8 + x = -9.433981132

Solving
8 + x = -9.433981132

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -9.433981132 + -8

Combine like terms: 8 + -8 = 0
0 + x = -9.433981132 + -8
x = -9.433981132 + -8

Combine like terms: -9.433981132 + -8 = -17.433981132
x = -17.433981132

Simplifying
x = -17.433981132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.433981132, -17.433981132}

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