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Simplifying 2x + -4(x + 2) = x(2x + -1) Reorder the terms: 2x + -4(2 + x) = x(2x + -1) 2x + (2 * -4 + x * -4) = x(2x + -1) 2x + (-8 + -4x) = x(2x + -1) Reorder the terms: -8 + 2x + -4x = x(2x + -1) Combine like terms: 2x + -4x = -2x -8 + -2x = x(2x + -1) Reorder the terms: -8 + -2x = x(-1 + 2x) -8 + -2x = (-1 * x + 2x * x) -8 + -2x = (-1x + 2x2) Solving -8 + -2x = -1x + 2x2 Solving for variable 'x'. Combine like terms: -2x + x = -1x -8 + -1x + -2x2 = -1x + 2x2 + x + -2x2 Reorder the terms: -8 + -1x + -2x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 -8 + -1x + -2x2 = 0 + 2x2 + -2x2 -8 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + -1x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + x + 2x2)' equal to zero and attempt to solve: Simplifying 8 + x + 2x2 = 0 Solving 8 + x + 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 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 = -4 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -4 + 0.25 Combine like terms: -4 + 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 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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