8x^3+4x^2-28x=0

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Solution for 8x^3+4x^2-28x=0 equation:


Simplifying
8x3 + 4x2 + -28x = 0

Reorder the terms:
-28x + 4x2 + 8x3 = 0

Solving
-28x + 4x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-7 + x + 2x2) = 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 '(-7 + x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + x + 2x2 = 0 Solving -7 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 0.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 0.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 0.5x + x2 = 0 + 3.5 0.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 0.5x + x2 = 3.5 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. 0.5x + 0.25 + x2 = 3.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 3.5 + 0.25 Combine like terms: 3.5 + 0.25 = 3.75 0.25 + 0.5x + x2 = 3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 0.5) equal to 1.936491673 and -1.936491673.

Subproblem 1

x + 0.5 = 1.936491673 Simplifying x + 0.5 = 1.936491673 Reorder the terms: 0.5 + x = 1.936491673 Solving 0.5 + x = 1.936491673 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 = 1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.936491673 + -0.5 x = 1.936491673 + -0.5 Combine like terms: 1.936491673 + -0.5 = 1.436491673 x = 1.436491673 Simplifying x = 1.436491673

Subproblem 2

x + 0.5 = -1.936491673 Simplifying x + 0.5 = -1.936491673 Reorder the terms: 0.5 + x = -1.936491673 Solving 0.5 + x = -1.936491673 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 = -1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.936491673 + -0.5 x = -1.936491673 + -0.5 Combine like terms: -1.936491673 + -0.5 = -2.436491673 x = -2.436491673 Simplifying x = -2.436491673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.436491673, -2.436491673}

Solution

x = {0, 1.436491673, -2.436491673}

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