0.375x^2+x-80=0

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Solution for 0.375x^2+x-80=0 equation: 


Simplifying
0.375x2 + x + -80 = 0

Reorder the terms:
-80 + x + 0.375x2 = 0

Solving
-80 + x + 0.375x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.375'.
-213.3333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '213.3333333' to each side of the equation.
-213.3333333 + 2.666666667x + 213.3333333 + x2 = 0 + 213.3333333

Reorder the terms:
-213.3333333 + 213.3333333 + 2.666666667x + x2 = 0 + 213.3333333

Combine like terms: -213.3333333 + 213.3333333 = 0.0000000
0.0000000 + 2.666666667x + x2 = 0 + 213.3333333
2.666666667x + x2 = 0 + 213.3333333

Combine like terms: 0 + 213.3333333 = 213.3333333
2.666666667x + x2 = 213.3333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
2.666666667x + 0.25 + x2 = 213.3333333 + 0.25

Reorder the terms:
0.25 + 2.666666667x + x2 = 213.3333333 + 0.25

Combine like terms: 213.3333333 + 0.25 = 213.5833333
0.25 + 2.666666667x + x2 = 213.5833333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 213.5833333

Calculate the square root of the right side: 14.614490525

Break this problem into two subproblems by setting 
(x + 0.5) equal to 14.614490525 and -14.614490525.


Subproblem 1
x + 0.5 = 14.614490525

Simplifying
x + 0.5 = 14.614490525

Reorder the terms:
0.5 + x = 14.614490525

Solving
0.5 + x = 14.614490525

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 14.614490525 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 14.614490525 + -0.5
x = 14.614490525 + -0.5

Combine like terms: 14.614490525 + -0.5 = 14.114490525
x = 14.114490525

Simplifying
x = 14.114490525


Subproblem 2
x + 0.5 = -14.614490525

Simplifying
x + 0.5 = -14.614490525

Reorder the terms:
0.5 + x = -14.614490525

Solving
0.5 + x = -14.614490525

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -14.614490525 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -14.614490525 + -0.5
x = -14.614490525 + -0.5

Combine like terms: -14.614490525 + -0.5 = -15.114490525
x = -15.114490525

Simplifying
x = -15.114490525


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.114490525, -15.114490525}

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