x^2+3x-90=0

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Solution for x^2+3x-90=0 equation: 


Simplifying
x2 + 3x + -90 = 0

Reorder the terms:
-90 + 3x + x2 = 0

Solving
-90 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 3x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 3x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 3x + x2 = 0 + 90
3x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
3x + x2 = 90

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 90 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 90 + 2.25

Combine like terms: 90 + 2.25 = 92.25
2.25 + 3x + x2 = 92.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + 1.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
x + 1.5 = 9.604686356

Simplifying
x + 1.5 = 9.604686356

Reorder the terms:
1.5 + x = 9.604686356

Solving
1.5 + x = 9.604686356

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 9.604686356 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 9.604686356 + -1.5
x = 9.604686356 + -1.5

Combine like terms: 9.604686356 + -1.5 = 8.104686356
x = 8.104686356

Simplifying
x = 8.104686356


Subproblem 2
x + 1.5 = -9.604686356

Simplifying
x + 1.5 = -9.604686356

Reorder the terms:
1.5 + x = -9.604686356

Solving
1.5 + x = -9.604686356

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -9.604686356 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -9.604686356 + -1.5
x = -9.604686356 + -1.5

Combine like terms: -9.604686356 + -1.5 = -11.104686356
x = -11.104686356

Simplifying
x = -11.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.104686356, -11.104686356}

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