2x^2-90x-450=0

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Solution for 2x^2-90x-450=0 equation: 


Simplifying
2x2 + -90x + -450 = 0

Reorder the terms:
-450 + -90x + 2x2 = 0

Solving
-450 + -90x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-225 + -45x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-225 + -45x + x2)' equal to zero and attempt to solve:

Simplifying
-225 + -45x + x2 = 0

Solving
-225 + -45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -45x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -45x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -45x + x2 = 0 + 225
-45x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-45x + x2 = 225

The x term is -45x.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45x + 506.25 + x2 = 225 + 506.25

Reorder the terms:
506.25 + -45x + x2 = 225 + 506.25

Combine like terms: 225 + 506.25 = 731.25
506.25 + -45x + x2 = 731.25

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 731.25

Calculate the square root of the right side: 27.041634566

Break this problem into two subproblems by setting 
(x + -22.5) equal to 27.041634566 and -27.041634566.


Subproblem 1
x + -22.5 = 27.041634566

Simplifying
x + -22.5 = 27.041634566

Reorder the terms:
-22.5 + x = 27.041634566

Solving
-22.5 + x = 27.041634566

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = 27.041634566 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = 27.041634566 + 22.5
x = 27.041634566 + 22.5

Combine like terms: 27.041634566 + 22.5 = 49.541634566
x = 49.541634566

Simplifying
x = 49.541634566


Subproblem 2
x + -22.5 = -27.041634566

Simplifying
x + -22.5 = -27.041634566

Reorder the terms:
-22.5 + x = -27.041634566

Solving
-22.5 + x = -27.041634566

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = -27.041634566 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = -27.041634566 + 22.5
x = -27.041634566 + 22.5

Combine like terms: -27.041634566 + 22.5 = -4.541634566
x = -4.541634566

Simplifying
x = -4.541634566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {49.541634566, -4.541634566}
Solution
x = {49.541634566, -4.541634566}

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