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Simplifying 2x + -4x + -4 = (2x + -2)(x + 1) Reorder the terms: -4 + 2x + -4x = (2x + -2)(x + 1) Combine like terms: 2x + -4x = -2x -4 + -2x = (2x + -2)(x + 1) Reorder the terms: -4 + -2x = (-2 + 2x)(x + 1) Reorder the terms: -4 + -2x = (-2 + 2x)(1 + x) Multiply (-2 + 2x) * (1 + x) -4 + -2x = (-2(1 + x) + 2x * (1 + x)) -4 + -2x = ((1 * -2 + x * -2) + 2x * (1 + x)) -4 + -2x = ((-2 + -2x) + 2x * (1 + x)) -4 + -2x = (-2 + -2x + (1 * 2x + x * 2x)) -4 + -2x = (-2 + -2x + (2x + 2x2)) Combine like terms: -2x + 2x = 0 -4 + -2x = (-2 + 0 + 2x2) -4 + -2x = (-2 + 2x2) Solving -4 + -2x = -2 + 2x2 Solving for variable 'x'. Reorder the terms: -4 + 2 + -2x + -2x2 = -2 + 2x2 + 2 + -2x2 Combine like terms: -4 + 2 = -2 -2 + -2x + -2x2 = -2 + 2x2 + 2 + -2x2 Reorder the terms: -2 + -2x + -2x2 = -2 + 2 + 2x2 + -2x2 Combine like terms: -2 + 2 = 0 -2 + -2x + -2x2 = 0 + 2x2 + -2x2 -2 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + x + x2)' equal to zero and attempt to solve: Simplifying 1 + x + x2 = 0 Solving 1 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x + x2 = 0 + -1 x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x + x2 = -1 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. x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 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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