36x^3-240x^2+100x=0

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Solution for 36x^3-240x^2+100x=0 equation:


Simplifying
36x3 + -240x2 + 100x = 0

Reorder the terms:
100x + -240x2 + 36x3 = 0

Solving
100x + -240x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(25 + -60x + 9x2) = 0

Ignore the factor 4.

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 '(25 + -60x + 9x2)' equal to zero and attempt to solve: Simplifying 25 + -60x + 9x2 = 0 Solving 25 + -60x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.777777778 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + -6.666666667x + -2.777777778 + x2 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + -6.666666667x + x2 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + -6.666666667x + x2 = 0 + -2.777777778 -6.666666667x + x2 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 -6.666666667x + x2 = -2.777777778 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = -2.777777778 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = -2.777777778 + 11.11111112 Combine like terms: -2.777777778 + 11.11111112 = 8.333333342 11.11111112 + -6.666666667x + x2 = 8.333333342 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 8.333333342 Calculate the square root of the right side: 2.886751347 Break this problem into two subproblems by setting (x + -3.333333334) equal to 2.886751347 and -2.886751347.

Subproblem 1

x + -3.333333334 = 2.886751347 Simplifying x + -3.333333334 = 2.886751347 Reorder the terms: -3.333333334 + x = 2.886751347 Solving -3.333333334 + x = 2.886751347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 2.886751347 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 2.886751347 + 3.333333334 x = 2.886751347 + 3.333333334 Combine like terms: 2.886751347 + 3.333333334 = 6.220084681 x = 6.220084681 Simplifying x = 6.220084681

Subproblem 2

x + -3.333333334 = -2.886751347 Simplifying x + -3.333333334 = -2.886751347 Reorder the terms: -3.333333334 + x = -2.886751347 Solving -3.333333334 + x = -2.886751347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -2.886751347 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -2.886751347 + 3.333333334 x = -2.886751347 + 3.333333334 Combine like terms: -2.886751347 + 3.333333334 = 0.446581987 x = 0.446581987 Simplifying x = 0.446581987

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.220084681, 0.446581987}

Solution

x = {0, 6.220084681, 0.446581987}

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