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Simplifying -2x(x + -2) + -4x = 3(x + -4) + 20 Reorder the terms: -2x(-2 + x) + -4x = 3(x + -4) + 20 (-2 * -2x + x * -2x) + -4x = 3(x + -4) + 20 (4x + -2x2) + -4x = 3(x + -4) + 20 Reorder the terms: 4x + -4x + -2x2 = 3(x + -4) + 20 Combine like terms: 4x + -4x = 0 0 + -2x2 = 3(x + -4) + 20 -2x2 = 3(x + -4) + 20 Reorder the terms: -2x2 = 3(-4 + x) + 20 -2x2 = (-4 * 3 + x * 3) + 20 -2x2 = (-12 + 3x) + 20 Reorder the terms: -2x2 = -12 + 20 + 3x Combine like terms: -12 + 20 = 8 -2x2 = 8 + 3x Solving -2x2 = 8 + 3x Solving for variable 'x'. Reorder the terms: -8 + -3x + -2x2 = 8 + 3x + -8 + -3x Reorder the terms: -8 + -3x + -2x2 = 8 + -8 + 3x + -3x Combine like terms: 8 + -8 = 0 -8 + -3x + -2x2 = 0 + 3x + -3x -8 + -3x + -2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -8 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 8 + 3x + 2x2 = 0 Solving 8 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 1.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 1.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 1.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 1.5x + x2 = 0 + -4 1.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 1.5x + x2 = -4 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -4 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -4 + 0.5625 Combine like terms: -4 + 0.5625 = -3.4375 0.5625 + 1.5x + x2 = -3.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -3.4375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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