3(90-x(180-x))=10

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Solution for 3(90-x(180-x))=10 equation:


Simplifying
3(90 + -1x(180 + -1x)) = 10
3(90 + (180 * -1x + -1x * -1x)) = 10
3(90 + (-180x + 1x2)) = 10
(90 * 3 + -180x * 3 + 1x2 * 3) = 10
(270 + -540x + 3x2) = 10

Solving
270 + -540x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
270 + -10 + -540x + 3x2 = 10 + -10

Combine like terms: 270 + -10 = 260
260 + -540x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
260 + -540x + 3x2 = 0

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

Divide each side by '3'.
86.66666667 + -180x + x2 = 0

Move the constant term to the right:

Add '-86.66666667' to each side of the equation.
86.66666667 + -180x + -86.66666667 + x2 = 0 + -86.66666667

Reorder the terms:
86.66666667 + -86.66666667 + -180x + x2 = 0 + -86.66666667

Combine like terms: 86.66666667 + -86.66666667 = 0.00000000
0.00000000 + -180x + x2 = 0 + -86.66666667
-180x + x2 = 0 + -86.66666667

Combine like terms: 0 + -86.66666667 = -86.66666667
-180x + x2 = -86.66666667

The x term is -180x.  Take half its coefficient (-90).
Square it (8100) and add it to both sides.

Add '8100' to each side of the equation.
-180x + 8100 + x2 = -86.66666667 + 8100

Reorder the terms:
8100 + -180x + x2 = -86.66666667 + 8100

Combine like terms: -86.66666667 + 8100 = 8013.33333333
8100 + -180x + x2 = 8013.33333333

Factor a perfect square on the left side:
(x + -90)(x + -90) = 8013.33333333

Calculate the square root of the right side: 89.517223669

Break this problem into two subproblems by setting 
(x + -90) equal to 89.517223669 and -89.517223669.

Subproblem 1

x + -90 = 89.517223669 Simplifying x + -90 = 89.517223669 Reorder the terms: -90 + x = 89.517223669 Solving -90 + x = 89.517223669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 89.517223669 + 90 Combine like terms: -90 + 90 = 0 0 + x = 89.517223669 + 90 x = 89.517223669 + 90 Combine like terms: 89.517223669 + 90 = 179.517223669 x = 179.517223669 Simplifying x = 179.517223669

Subproblem 2

x + -90 = -89.517223669 Simplifying x + -90 = -89.517223669 Reorder the terms: -90 + x = -89.517223669 Solving -90 + x = -89.517223669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -89.517223669 + 90 Combine like terms: -90 + 90 = 0 0 + x = -89.517223669 + 90 x = -89.517223669 + 90 Combine like terms: -89.517223669 + 90 = 0.482776331 x = 0.482776331 Simplifying x = 0.482776331

Solution

The solution to the problem is based on the solutions from the subproblems. x = {179.517223669, 0.482776331}

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