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Simplifying 4x(2x + -1) = 2(3x + -2) Reorder the terms: 4x(-1 + 2x) = 2(3x + -2) (-1 * 4x + 2x * 4x) = 2(3x + -2) (-4x + 8x2) = 2(3x + -2) Reorder the terms: -4x + 8x2 = 2(-2 + 3x) -4x + 8x2 = (-2 * 2 + 3x * 2) -4x + 8x2 = (-4 + 6x) Solving -4x + 8x2 = -4 + 6x Solving for variable 'x'. Reorder the terms: 4 + -4x + -6x + 8x2 = -4 + 6x + 4 + -6x Combine like terms: -4x + -6x = -10x 4 + -10x + 8x2 = -4 + 6x + 4 + -6x Reorder the terms: 4 + -10x + 8x2 = -4 + 4 + 6x + -6x Combine like terms: -4 + 4 = 0 4 + -10x + 8x2 = 0 + 6x + -6x 4 + -10x + 8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 4 + -10x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -5x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -5x + 4x2)' equal to zero and attempt to solve: Simplifying 2 + -5x + 4x2 = 0 Solving 2 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.25x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.25x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.25x + x2 = 0 + -0.5 -1.25x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.25x + x2 = -0.5 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.5 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.5 + 0.390625 Combine like terms: -0.5 + 0.390625 = -0.109375 0.390625 + -1.25x + x2 = -0.109375 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -0.109375 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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