(2x^3-4x^2+6x)+(2x^3+8x^2-11x)=

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Solution for (2x^3-4x^2+6x)+(2x^3+8x^2-11x)= equation:


Simplifying
(2x3 + -4x2 + 6x) + (2x3 + 8x2 + -11x) = 0

Reorder the terms:
(6x + -4x2 + 2x3) + (2x3 + 8x2 + -11x) = 0

Remove parenthesis around (6x + -4x2 + 2x3)
6x + -4x2 + 2x3 + (2x3 + 8x2 + -11x) = 0

Reorder the terms:
6x + -4x2 + 2x3 + (-11x + 8x2 + 2x3) = 0

Remove parenthesis around (-11x + 8x2 + 2x3)
6x + -4x2 + 2x3 + -11x + 8x2 + 2x3 = 0

Reorder the terms:
6x + -11x + -4x2 + 8x2 + 2x3 + 2x3 = 0

Combine like terms: 6x + -11x = -5x
-5x + -4x2 + 8x2 + 2x3 + 2x3 = 0

Combine like terms: -4x2 + 8x2 = 4x2
-5x + 4x2 + 2x3 + 2x3 = 0

Combine like terms: 2x3 + 2x3 = 4x3
-5x + 4x2 + 4x3 = 0

Solving
-5x + 4x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 4x + 4x2) = 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 '(-5 + 4x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + 4x + 4x2 = 0 Solving -5 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x + x2 = 0 + 1.25 x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 x + x2 = 1.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.25 + 0.25 Combine like terms: 1.25 + 0.25 = 1.5 1.25 + x2 = 1.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 0.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + 0.5 = 1.224744871 Simplifying x + 0.5 = 1.224744871 Reorder the terms: 0.5 + x = 1.224744871 Solving 0.5 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.224744871 + -0.5 x = 1.224744871 + -0.5 Combine like terms: 1.224744871 + -0.5 = 0.724744871 x = 0.724744871 Simplifying x = 0.724744871

Subproblem 2

x + 0.5 = -1.224744871 Simplifying x + 0.5 = -1.224744871 Reorder the terms: 0.5 + x = -1.224744871 Solving 0.5 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.224744871 + -0.5 x = -1.224744871 + -0.5 Combine like terms: -1.224744871 + -0.5 = -1.724744871 x = -1.724744871 Simplifying x = -1.724744871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.724744871, -1.724744871}

Solution

x = {0, 0.724744871, -1.724744871}

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