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Simplifying x(x + 2)(x + -4) = 3x + -1x2 Reorder the terms: x(2 + x)(x + -4) = 3x + -1x2 Reorder the terms: x(2 + x)(-4 + x) = 3x + -1x2 Multiply (2 + x) * (-4 + x) x(2(-4 + x) + x(-4 + x)) = 3x + -1x2 x((-4 * 2 + x * 2) + x(-4 + x)) = 3x + -1x2 x((-8 + 2x) + x(-4 + x)) = 3x + -1x2 x(-8 + 2x + (-4 * x + x * x)) = 3x + -1x2 x(-8 + 2x + (-4x + x2)) = 3x + -1x2 Combine like terms: 2x + -4x = -2x x(-8 + -2x + x2) = 3x + -1x2 (-8 * x + -2x * x + x2 * x) = 3x + -1x2 (-8x + -2x2 + x3) = 3x + -1x2 Solving -8x + -2x2 + x3 = 3x + -1x2 Solving for variable 'x'. Reorder the terms: -8x + -3x + -2x2 + x2 + x3 = 3x + -1x2 + -3x + x2 Combine like terms: -8x + -3x = -11x -11x + -2x2 + x2 + x3 = 3x + -1x2 + -3x + x2 Combine like terms: -2x2 + x2 = -1x2 -11x + -1x2 + x3 = 3x + -1x2 + -3x + x2 Reorder the terms: -11x + -1x2 + x3 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 -11x + -1x2 + x3 = 0 + -1x2 + x2 -11x + -1x2 + x3 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -11x + -1x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + -1x + x2) = 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 '(-11 + -1x + x2)' equal to zero and attempt to solve: Simplifying -11 + -1x + x2 = 0 Solving -11 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -1x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -1x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x + x2 = 0 + 11 -1x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -1x + x2 = 11 The x term is -1x. 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. -1x + 0.25 + x2 = 11 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 11 + 0.25 Combine like terms: 11 + 0.25 = 11.25 0.25 + -1x + x2 = 11.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -0.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -0.5 = 3.354101966 Simplifying x + -0.5 = 3.354101966 Reorder the terms: -0.5 + x = 3.354101966 Solving -0.5 + x = 3.354101966 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 = 3.354101966 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.354101966 + 0.5 x = 3.354101966 + 0.5 Combine like terms: 3.354101966 + 0.5 = 3.854101966 x = 3.854101966 Simplifying x = 3.854101966Subproblem 2
x + -0.5 = -3.354101966 Simplifying x + -0.5 = -3.354101966 Reorder the terms: -0.5 + x = -3.354101966 Solving -0.5 + x = -3.354101966 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 = -3.354101966 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.354101966 + 0.5 x = -3.354101966 + 0.5 Combine like terms: -3.354101966 + 0.5 = -2.854101966 x = -2.854101966 Simplifying x = -2.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.854101966, -2.854101966}Solution
x = {0, 3.854101966, -2.854101966}
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