-18x^3-10x^2+18x=0

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Solution for -18x^3-10x^2+18x=0 equation:


Simplifying
-18x3 + -10x2 + 18x = 0

Reorder the terms:
18x + -10x2 + -18x3 = 0

Solving
18x + -10x2 + -18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + -5x + -9x2) = 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 '(9 + -5x + -9x2)' equal to zero and attempt to solve: Simplifying 9 + -5x + -9x2 = 0 Solving 9 + -5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.5555555556x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.5555555556x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.5555555556x + x2 = 0 + 1 0.5555555556x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.5555555556x + x2 = 1 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 1 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 1 + 0.07716049384 Combine like terms: 1 + 0.07716049384 = 1.07716049384 0.07716049384 + 0.5555555556x + x2 = 1.07716049384 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 1.07716049384 Calculate the square root of the right side: 1.037863427 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 1.037863427 and -1.037863427.

Subproblem 1

x + 0.2777777778 = 1.037863427 Simplifying x + 0.2777777778 = 1.037863427 Reorder the terms: 0.2777777778 + x = 1.037863427 Solving 0.2777777778 + x = 1.037863427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 1.037863427 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 1.037863427 + -0.2777777778 x = 1.037863427 + -0.2777777778 Combine like terms: 1.037863427 + -0.2777777778 = 0.7600856492 x = 0.7600856492 Simplifying x = 0.7600856492

Subproblem 2

x + 0.2777777778 = -1.037863427 Simplifying x + 0.2777777778 = -1.037863427 Reorder the terms: 0.2777777778 + x = -1.037863427 Solving 0.2777777778 + x = -1.037863427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -1.037863427 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -1.037863427 + -0.2777777778 x = -1.037863427 + -0.2777777778 Combine like terms: -1.037863427 + -0.2777777778 = -1.3156412048 x = -1.3156412048 Simplifying x = -1.3156412048

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7600856492, -1.3156412048}

Solution

x = {0, 0.7600856492, -1.3156412048}

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