10x^3-8x^2-180x=0

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Solution for 10x^3-8x^2-180x=0 equation:


Simplifying
10x3 + -8x2 + -180x = 0

Reorder the terms:
-180x + -8x2 + 10x3 = 0

Solving
-180x + -8x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-90 + -4x + 5x2) = 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 '(-90 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying -90 + -4x + 5x2 = 0 Solving -90 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18 + -0.8x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -0.8x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -0.8x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -0.8x + x2 = 0 + 18 -0.8x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -0.8x + x2 = 18 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 18 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 18 + 0.16 Combine like terms: 18 + 0.16 = 18.16 0.16 + -0.8x + x2 = 18.16 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 18.16 Calculate the square root of the right side: 4.261455151 Break this problem into two subproblems by setting (x + -0.4) equal to 4.261455151 and -4.261455151.

Subproblem 1

x + -0.4 = 4.261455151 Simplifying x + -0.4 = 4.261455151 Reorder the terms: -0.4 + x = 4.261455151 Solving -0.4 + x = 4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 4.261455151 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 4.261455151 + 0.4 x = 4.261455151 + 0.4 Combine like terms: 4.261455151 + 0.4 = 4.661455151 x = 4.661455151 Simplifying x = 4.661455151

Subproblem 2

x + -0.4 = -4.261455151 Simplifying x + -0.4 = -4.261455151 Reorder the terms: -0.4 + x = -4.261455151 Solving -0.4 + x = -4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -4.261455151 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -4.261455151 + 0.4 x = -4.261455151 + 0.4 Combine like terms: -4.261455151 + 0.4 = -3.861455151 x = -3.861455151 Simplifying x = -3.861455151

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.661455151, -3.861455151}

Solution

x = {0, 4.661455151, -3.861455151}

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