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Simplifying 2x3 = 8x + x2 Solving 2x3 = 8x + x2 Solving for variable 'x'. Reorder the terms: -8x + -1x2 + 2x3 = 8x + x2 + -8x + -1x2 Reorder the terms: -8x + -1x2 + 2x3 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -8x + -1x2 + 2x3 = 0 + x2 + -1x2 -8x + -1x2 + 2x3 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8x + -1x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + -1x + 2x2) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(-8 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -8 + -1x + 2x2 = 0 Solving -8 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -0.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.5x + x2 = 0 + 4 -0.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.5x + x2 = 4 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 4 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4 + 0.0625 Combine like terms: 4 + 0.0625 = 4.0625 0.0625 + -0.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -0.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -0.25 = 2.015564437 Simplifying x + -0.25 = 2.015564437 Reorder the terms: -0.25 + x = 2.015564437 Solving -0.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.015564437 + 0.25 x = 2.015564437 + 0.25 Combine like terms: 2.015564437 + 0.25 = 2.265564437 x = 2.265564437 Simplifying x = 2.265564437Subproblem 2
x + -0.25 = -2.015564437 Simplifying x + -0.25 = -2.015564437 Reorder the terms: -0.25 + x = -2.015564437 Solving -0.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.015564437 + 0.25 x = -2.015564437 + 0.25 Combine like terms: -2.015564437 + 0.25 = -1.765564437 x = -1.765564437 Simplifying x = -1.765564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.265564437, -1.765564437}Solution
x = {0, 2.265564437, -1.765564437}
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