2x^2+6x-90=0

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Solution for 2x^2+6x-90=0 equation: 


Simplifying
2x2 + 6x + -90 = 0

Reorder the terms:
-90 + 6x + 2x2 = 0

Solving
-90 + 6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 3x + x2 = 0

Solving
-45 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 3x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 3x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 3x + x2 = 0 + 45
3x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
3x + x2 = 45

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 = 45 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 45 + 2.25

Combine like terms: 45 + 2.25 = 47.25
2.25 + 3x + x2 = 47.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
x + 1.5 = 6.873863542

Simplifying
x + 1.5 = 6.873863542

Reorder the terms:
1.5 + x = 6.873863542

Solving
1.5 + x = 6.873863542

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 = 6.873863542 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 6.873863542 + -1.5
x = 6.873863542 + -1.5

Combine like terms: 6.873863542 + -1.5 = 5.373863542
x = 5.373863542

Simplifying
x = 5.373863542


Subproblem 2
x + 1.5 = -6.873863542

Simplifying
x + 1.5 = -6.873863542

Reorder the terms:
1.5 + x = -6.873863542

Solving
1.5 + x = -6.873863542

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 = -6.873863542 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -6.873863542 + -1.5
x = -6.873863542 + -1.5

Combine like terms: -6.873863542 + -1.5 = -8.373863542
x = -8.373863542

Simplifying
x = -8.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.373863542, -8.373863542}
Solution
x = {5.373863542, -8.373863542}

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