2x^2(18-x)=x(40-2x)(20-2x)

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Solution for 2x^2(18-x)=x(40-2x)(20-2x) equation:


Simplifying
2x2(18 + -1x) = x(40 + -2x)(20 + -2x)
(18 * 2x2 + -1x * 2x2) = x(40 + -2x)(20 + -2x)
(36x2 + -2x3) = x(40 + -2x)(20 + -2x)

Multiply (40 + -2x) * (20 + -2x)
36x2 + -2x3 = x(40(20 + -2x) + -2x * (20 + -2x))
36x2 + -2x3 = x((20 * 40 + -2x * 40) + -2x * (20 + -2x))
36x2 + -2x3 = x((800 + -80x) + -2x * (20 + -2x))
36x2 + -2x3 = x(800 + -80x + (20 * -2x + -2x * -2x))
36x2 + -2x3 = x(800 + -80x + (-40x + 4x2))

Combine like terms: -80x + -40x = -120x
36x2 + -2x3 = x(800 + -120x + 4x2)
36x2 + -2x3 = (800 * x + -120x * x + 4x2 * x)
36x2 + -2x3 = (800x + -120x2 + 4x3)

Solving
36x2 + -2x3 = 800x + -120x2 + 4x3

Solving for variable 'x'.

Reorder the terms:
-800x + 36x2 + 120x2 + -2x3 + -4x3 = 800x + -120x2 + 4x3 + -800x + 120x2 + -4x3

Combine like terms: 36x2 + 120x2 = 156x2
-800x + 156x2 + -2x3 + -4x3 = 800x + -120x2 + 4x3 + -800x + 120x2 + -4x3

Combine like terms: -2x3 + -4x3 = -6x3
-800x + 156x2 + -6x3 = 800x + -120x2 + 4x3 + -800x + 120x2 + -4x3

Reorder the terms:
-800x + 156x2 + -6x3 = 800x + -800x + -120x2 + 120x2 + 4x3 + -4x3

Combine like terms: 800x + -800x = 0
-800x + 156x2 + -6x3 = 0 + -120x2 + 120x2 + 4x3 + -4x3
-800x + 156x2 + -6x3 = -120x2 + 120x2 + 4x3 + -4x3

Combine like terms: -120x2 + 120x2 = 0
-800x + 156x2 + -6x3 = 0 + 4x3 + -4x3
-800x + 156x2 + -6x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-800x + 156x2 + -6x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-400 + 78x + -3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-400 + 78x + -3x2)' equal to zero and attempt to solve: Simplifying -400 + 78x + -3x2 = 0 Solving -400 + 78x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 133.3333333 + -26x + x2 = 0 Move the constant term to the right: Add '-133.3333333' to each side of the equation. 133.3333333 + -26x + -133.3333333 + x2 = 0 + -133.3333333 Reorder the terms: 133.3333333 + -133.3333333 + -26x + x2 = 0 + -133.3333333 Combine like terms: 133.3333333 + -133.3333333 = 0.0000000 0.0000000 + -26x + x2 = 0 + -133.3333333 -26x + x2 = 0 + -133.3333333 Combine like terms: 0 + -133.3333333 = -133.3333333 -26x + x2 = -133.3333333 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -133.3333333 + 169 Reorder the terms: 169 + -26x + x2 = -133.3333333 + 169 Combine like terms: -133.3333333 + 169 = 35.6666667 169 + -26x + x2 = 35.6666667 Factor a perfect square on the left side: (x + -13)(x + -13) = 35.6666667 Calculate the square root of the right side: 5.972157625 Break this problem into two subproblems by setting (x + -13) equal to 5.972157625 and -5.972157625.

Subproblem 1

x + -13 = 5.972157625 Simplifying x + -13 = 5.972157625 Reorder the terms: -13 + x = 5.972157625 Solving -13 + x = 5.972157625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 5.972157625 + 13 Combine like terms: -13 + 13 = 0 0 + x = 5.972157625 + 13 x = 5.972157625 + 13 Combine like terms: 5.972157625 + 13 = 18.972157625 x = 18.972157625 Simplifying x = 18.972157625

Subproblem 2

x + -13 = -5.972157625 Simplifying x + -13 = -5.972157625 Reorder the terms: -13 + x = -5.972157625 Solving -13 + x = -5.972157625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -5.972157625 + 13 Combine like terms: -13 + 13 = 0 0 + x = -5.972157625 + 13 x = -5.972157625 + 13 Combine like terms: -5.972157625 + 13 = 7.027842375 x = 7.027842375 Simplifying x = 7.027842375

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.972157625, 7.027842375}

Solution

x = {0, 18.972157625, 7.027842375}

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