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Simplifying (2x + 3) + (2x + -3) = (8x + 6)(x + -1) + 22 Reorder the terms: (3 + 2x) + (2x + -3) = (8x + 6)(x + -1) + 22 Remove parenthesis around (3 + 2x) 3 + 2x + (2x + -3) = (8x + 6)(x + -1) + 22 Reorder the terms: 3 + 2x + (-3 + 2x) = (8x + 6)(x + -1) + 22 Remove parenthesis around (-3 + 2x) 3 + 2x + -3 + 2x = (8x + 6)(x + -1) + 22 Reorder the terms: 3 + -3 + 2x + 2x = (8x + 6)(x + -1) + 22 Combine like terms: 3 + -3 = 0 0 + 2x + 2x = (8x + 6)(x + -1) + 22 2x + 2x = (8x + 6)(x + -1) + 22 Combine like terms: 2x + 2x = 4x 4x = (8x + 6)(x + -1) + 22 Reorder the terms: 4x = (6 + 8x)(x + -1) + 22 Reorder the terms: 4x = (6 + 8x)(-1 + x) + 22 Multiply (6 + 8x) * (-1 + x) 4x = (6(-1 + x) + 8x * (-1 + x)) + 22 4x = ((-1 * 6 + x * 6) + 8x * (-1 + x)) + 22 4x = ((-6 + 6x) + 8x * (-1 + x)) + 22 4x = (-6 + 6x + (-1 * 8x + x * 8x)) + 22 4x = (-6 + 6x + (-8x + 8x2)) + 22 Combine like terms: 6x + -8x = -2x 4x = (-6 + -2x + 8x2) + 22 Reorder the terms: 4x = -6 + 22 + -2x + 8x2 Combine like terms: -6 + 22 = 16 4x = 16 + -2x + 8x2 Solving 4x = 16 + -2x + 8x2 Solving for variable 'x'. Reorder the terms: -16 + 4x + 2x + -8x2 = 16 + -2x + 8x2 + -16 + 2x + -8x2 Combine like terms: 4x + 2x = 6x -16 + 6x + -8x2 = 16 + -2x + 8x2 + -16 + 2x + -8x2 Reorder the terms: -16 + 6x + -8x2 = 16 + -16 + -2x + 2x + 8x2 + -8x2 Combine like terms: 16 + -16 = 0 -16 + 6x + -8x2 = 0 + -2x + 2x + 8x2 + -8x2 -16 + 6x + -8x2 = -2x + 2x + 8x2 + -8x2 Combine like terms: -2x + 2x = 0 -16 + 6x + -8x2 = 0 + 8x2 + -8x2 -16 + 6x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -16 + 6x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 3x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying -8 + 3x + -4x2 = 0 Solving -8 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2 + -0.75x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.75x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -0.75x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.75x + x2 = 0 + -2 -0.75x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.75x + x2 = -2 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 = -2 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -2 + 0.140625 Combine like terms: -2 + 0.140625 = -1.859375 0.140625 + -0.75x + x2 = -1.859375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -1.859375 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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