3x(90-x)=122

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Solution for 3x(90-x)=122 equation: 


Simplifying
3x(90 + -1x) = 122
(90 * 3x + -1x * 3x) = 122
(270x + -3x2) = 122

Solving
270x + -3x2 = 122

Solving for variable 'x'.

Reorder the terms:
-122 + 270x + -3x2 = 122 + -122

Combine like terms: 122 + -122 = 0
-122 + 270x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
40.66666667 + -90x + x2 = 0

Move the constant term to the right:

Add '-40.66666667' to each side of the equation.
40.66666667 + -90x + -40.66666667 + x2 = 0 + -40.66666667

Reorder the terms:
40.66666667 + -40.66666667 + -90x + x2 = 0 + -40.66666667

Combine like terms: 40.66666667 + -40.66666667 = 0.00000000
0.00000000 + -90x + x2 = 0 + -40.66666667
-90x + x2 = 0 + -40.66666667

Combine like terms: 0 + -40.66666667 = -40.66666667
-90x + x2 = -40.66666667

The x term is -90x.  Take half its coefficient (-45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
-90x + 2025 + x2 = -40.66666667 + 2025

Reorder the terms:
2025 + -90x + x2 = -40.66666667 + 2025

Combine like terms: -40.66666667 + 2025 = 1984.33333333
2025 + -90x + x2 = 1984.33333333

Factor a perfect square on the left side:
(x + -45)(x + -45) = 1984.33333333

Calculate the square root of the right side: 44.545856523

Break this problem into two subproblems by setting 
(x + -45) equal to 44.545856523 and -44.545856523.


Subproblem 1
x + -45 = 44.545856523

Simplifying
x + -45 = 44.545856523

Reorder the terms:
-45 + x = 44.545856523

Solving
-45 + x = 44.545856523

Solving for variable 'x'.

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

Add '45' to each side of the equation.
-45 + 45 + x = 44.545856523 + 45

Combine like terms: -45 + 45 = 0
0 + x = 44.545856523 + 45
x = 44.545856523 + 45

Combine like terms: 44.545856523 + 45 = 89.545856523
x = 89.545856523

Simplifying
x = 89.545856523


Subproblem 2
x + -45 = -44.545856523

Simplifying
x + -45 = -44.545856523

Reorder the terms:
-45 + x = -44.545856523

Solving
-45 + x = -44.545856523

Solving for variable 'x'.

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

Add '45' to each side of the equation.
-45 + 45 + x = -44.545856523 + 45

Combine like terms: -45 + 45 = 0
0 + x = -44.545856523 + 45
x = -44.545856523 + 45

Combine like terms: -44.545856523 + 45 = 0.454143477
x = 0.454143477

Simplifying
x = 0.454143477


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {89.545856523, 0.454143477}

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