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Simplifying 4x(-2x + 1) = 6 + -1(2x + -4) Reorder the terms: 4x(1 + -2x) = 6 + -1(2x + -4) (1 * 4x + -2x * 4x) = 6 + -1(2x + -4) (4x + -8x2) = 6 + -1(2x + -4) Reorder the terms: 4x + -8x2 = 6 + -1(-4 + 2x) 4x + -8x2 = 6 + (-4 * -1 + 2x * -1) 4x + -8x2 = 6 + (4 + -2x) Combine like terms: 6 + 4 = 10 4x + -8x2 = 10 + -2x Solving 4x + -8x2 = 10 + -2x Solving for variable 'x'. Reorder the terms: -10 + 4x + 2x + -8x2 = 10 + -2x + -10 + 2x Combine like terms: 4x + 2x = 6x -10 + 6x + -8x2 = 10 + -2x + -10 + 2x Reorder the terms: -10 + 6x + -8x2 = 10 + -10 + -2x + 2x Combine like terms: 10 + -10 = 0 -10 + 6x + -8x2 = 0 + -2x + 2x -10 + 6x + -8x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -10 + 6x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 3x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + -4x2 = 0 Solving -5 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -0.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -0.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -0.75x + x2 = 0 + -1.25 -0.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -0.75x + x2 = -1.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -1.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -1.25 + 0.140625 Combine like terms: -1.25 + 0.140625 = -1.109375 0.140625 + -0.75x + x2 = -1.109375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -1.109375 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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