795=90*x+5*x^2

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Solution for 795=90*x+5*x^2 equation: 


Simplifying
795 = 90x + 5x2

Solving
795 = 90x + 5x2

Solving for variable 'x'.

Reorder the terms:
795 + -90x + -5x2 = 90x + -90x + 5x2 + -5x2

Combine like terms: 90x + -90x = 0
795 + -90x + -5x2 = 0 + 5x2 + -5x2
795 + -90x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
795 + -90x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(159 + -18x + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(159 + -18x + -1x2)' equal to zero and attempt to solve:

Simplifying
159 + -18x + -1x2 = 0

Solving
159 + -18x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-159 + 18x + x2 = 0

Move the constant term to the right:

Add '159' to each side of the equation.
-159 + 18x + 159 + x2 = 0 + 159

Reorder the terms:
-159 + 159 + 18x + x2 = 0 + 159

Combine like terms: -159 + 159 = 0
0 + 18x + x2 = 0 + 159
18x + x2 = 0 + 159

Combine like terms: 0 + 159 = 159
18x + x2 = 159

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 = 159 + 81

Reorder the terms:
81 + 18x + x2 = 159 + 81

Combine like terms: 159 + 81 = 240
81 + 18x + x2 = 240

Factor a perfect square on the left side:
(x + 9)(x + 9) = 240

Calculate the square root of the right side: 15.491933385

Break this problem into two subproblems by setting 
(x + 9) equal to 15.491933385 and -15.491933385.


Subproblem 1
x + 9 = 15.491933385

Simplifying
x + 9 = 15.491933385

Reorder the terms:
9 + x = 15.491933385

Solving
9 + x = 15.491933385

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 = 15.491933385 + -9

Combine like terms: 9 + -9 = 0
0 + x = 15.491933385 + -9
x = 15.491933385 + -9

Combine like terms: 15.491933385 + -9 = 6.491933385
x = 6.491933385

Simplifying
x = 6.491933385


Subproblem 2
x + 9 = -15.491933385

Simplifying
x + 9 = -15.491933385

Reorder the terms:
9 + x = -15.491933385

Solving
9 + x = -15.491933385

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 = -15.491933385 + -9

Combine like terms: 9 + -9 = 0
0 + x = -15.491933385 + -9
x = -15.491933385 + -9

Combine like terms: -15.491933385 + -9 = -24.491933385
x = -24.491933385

Simplifying
x = -24.491933385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.491933385, -24.491933385}
Solution
x = {6.491933385, -24.491933385}

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