.5x^2+2.5x-90=0

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Solution for .5x^2+2.5x-90=0 equation: 


Simplifying
0.5x2 + 2.5x + -90 = 0

Reorder the terms:
-90 + 2.5x + 0.5x2 = 0

Solving
-90 + 2.5x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-180 + 5x + x2 = 0

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 5x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 5x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 5x + x2 = 0 + 180
5x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
5x + x2 = 180

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 180 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 180 + 6.25

Combine like terms: 180 + 6.25 = 186.25
6.25 + 5x + x2 = 186.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 186.25

Calculate the square root of the right side: 13.647344064

Break this problem into two subproblems by setting 
(x + 2.5) equal to 13.647344064 and -13.647344064.


Subproblem 1
x + 2.5 = 13.647344064

Simplifying
x + 2.5 = 13.647344064

Reorder the terms:
2.5 + x = 13.647344064

Solving
2.5 + x = 13.647344064

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 13.647344064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 13.647344064 + -2.5
x = 13.647344064 + -2.5

Combine like terms: 13.647344064 + -2.5 = 11.147344064
x = 11.147344064

Simplifying
x = 11.147344064


Subproblem 2
x + 2.5 = -13.647344064

Simplifying
x + 2.5 = -13.647344064

Reorder the terms:
2.5 + x = -13.647344064

Solving
2.5 + x = -13.647344064

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -13.647344064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -13.647344064 + -2.5
x = -13.647344064 + -2.5

Combine like terms: -13.647344064 + -2.5 = -16.147344064
x = -16.147344064

Simplifying
x = -16.147344064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.147344064, -16.147344064}

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