5x^2-90x-1200=0

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Solution for 5x^2-90x-1200=0 equation: 


Simplifying
5x2 + -90x + -1200 = 0

Reorder the terms:
-1200 + -90x + 5x2 = 0

Solving
-1200 + -90x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-240 + -18x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-240 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
-240 + -18x + x2 = 0

Solving
-240 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + -18x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + -18x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + -18x + x2 = 0 + 240
-18x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
-18x + x2 = 240

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 240 + 81

Reorder the terms:
81 + -18x + x2 = 240 + 81

Combine like terms: 240 + 81 = 321
81 + -18x + x2 = 321

Factor a perfect square on the left side:
(x + -9)(x + -9) = 321

Calculate the square root of the right side: 17.916472867

Break this problem into two subproblems by setting 
(x + -9) equal to 17.916472867 and -17.916472867.


Subproblem 1
x + -9 = 17.916472867

Simplifying
x + -9 = 17.916472867

Reorder the terms:
-9 + x = 17.916472867

Solving
-9 + x = 17.916472867

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 17.916472867 + 9

Combine like terms: -9 + 9 = 0
0 + x = 17.916472867 + 9
x = 17.916472867 + 9

Combine like terms: 17.916472867 + 9 = 26.916472867
x = 26.916472867

Simplifying
x = 26.916472867


Subproblem 2
x + -9 = -17.916472867

Simplifying
x + -9 = -17.916472867

Reorder the terms:
-9 + x = -17.916472867

Solving
-9 + x = -17.916472867

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -17.916472867 + 9

Combine like terms: -9 + 9 = 0
0 + x = -17.916472867 + 9
x = -17.916472867 + 9

Combine like terms: -17.916472867 + 9 = -8.916472867
x = -8.916472867

Simplifying
x = -8.916472867


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.916472867, -8.916472867}
Solution
x = {26.916472867, -8.916472867}

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