44x^3-6x^2-x=0

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Solution for 44x^3-6x^2-x=0 equation:


Simplifying
44x3 + -6x2 + -1x = 0

Reorder the terms:
-1x + -6x2 + 44x3 = 0

Solving
-1x + -6x2 + 44x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + -6x + 44x2) = 0

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 '(-1 + -6x + 44x2)' equal to zero and attempt to solve: Simplifying -1 + -6x + 44x2 = 0 Solving -1 + -6x + 44x2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.02272727273 + -0.1363636364x + x2 = 0 Move the constant term to the right: Add '0.02272727273' to each side of the equation. -0.02272727273 + -0.1363636364x + 0.02272727273 + x2 = 0 + 0.02272727273 Reorder the terms: -0.02272727273 + 0.02272727273 + -0.1363636364x + x2 = 0 + 0.02272727273 Combine like terms: -0.02272727273 + 0.02272727273 = 0.00000000000 0.00000000000 + -0.1363636364x + x2 = 0 + 0.02272727273 -0.1363636364x + x2 = 0 + 0.02272727273 Combine like terms: 0 + 0.02272727273 = 0.02272727273 -0.1363636364x + x2 = 0.02272727273 The x term is -0.1363636364x. Take half its coefficient (-0.0681818182). Square it (0.004648760333) and add it to both sides. Add '0.004648760333' to each side of the equation. -0.1363636364x + 0.004648760333 + x2 = 0.02272727273 + 0.004648760333 Reorder the terms: 0.004648760333 + -0.1363636364x + x2 = 0.02272727273 + 0.004648760333 Combine like terms: 0.02272727273 + 0.004648760333 = 0.027376033063 0.004648760333 + -0.1363636364x + x2 = 0.027376033063 Factor a perfect square on the left side: (x + -0.0681818182)(x + -0.0681818182) = 0.027376033063 Calculate the square root of the right side: 0.165457043 Break this problem into two subproblems by setting (x + -0.0681818182) equal to 0.165457043 and -0.165457043.

Subproblem 1

x + -0.0681818182 = 0.165457043 Simplifying x + -0.0681818182 = 0.165457043 Reorder the terms: -0.0681818182 + x = 0.165457043 Solving -0.0681818182 + x = 0.165457043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0681818182' to each side of the equation. -0.0681818182 + 0.0681818182 + x = 0.165457043 + 0.0681818182 Combine like terms: -0.0681818182 + 0.0681818182 = 0.0000000000 0.0000000000 + x = 0.165457043 + 0.0681818182 x = 0.165457043 + 0.0681818182 Combine like terms: 0.165457043 + 0.0681818182 = 0.2336388612 x = 0.2336388612 Simplifying x = 0.2336388612

Subproblem 2

x + -0.0681818182 = -0.165457043 Simplifying x + -0.0681818182 = -0.165457043 Reorder the terms: -0.0681818182 + x = -0.165457043 Solving -0.0681818182 + x = -0.165457043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0681818182' to each side of the equation. -0.0681818182 + 0.0681818182 + x = -0.165457043 + 0.0681818182 Combine like terms: -0.0681818182 + 0.0681818182 = 0.0000000000 0.0000000000 + x = -0.165457043 + 0.0681818182 x = -0.165457043 + 0.0681818182 Combine like terms: -0.165457043 + 0.0681818182 = -0.0972752248 x = -0.0972752248 Simplifying x = -0.0972752248

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2336388612, -0.0972752248}

Solution

x = {0, 0.2336388612, -0.0972752248}

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