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Simplifying (2x + 3) * 2 + (2x + -3) * 2 = (8x + 6)(x + -1) + 22 Reorder the terms: (3 + 2x) * 2 + (2x + -3) * 2 = (8x + 6)(x + -1) + 22 Reorder the terms for easier multiplication: 2(3 + 2x) + (2x + -3) * 2 = (8x + 6)(x + -1) + 22 (3 * 2 + 2x * 2) + (2x + -3) * 2 = (8x + 6)(x + -1) + 22 (6 + 4x) + (2x + -3) * 2 = (8x + 6)(x + -1) + 22 Reorder the terms: 6 + 4x + (-3 + 2x) * 2 = (8x + 6)(x + -1) + 22 Reorder the terms for easier multiplication: 6 + 4x + 2(-3 + 2x) = (8x + 6)(x + -1) + 22 6 + 4x + (-3 * 2 + 2x * 2) = (8x + 6)(x + -1) + 22 6 + 4x + (-6 + 4x) = (8x + 6)(x + -1) + 22 Reorder the terms: 6 + -6 + 4x + 4x = (8x + 6)(x + -1) + 22 Combine like terms: 6 + -6 = 0 0 + 4x + 4x = (8x + 6)(x + -1) + 22 4x + 4x = (8x + 6)(x + -1) + 22 Combine like terms: 4x + 4x = 8x 8x = (8x + 6)(x + -1) + 22 Reorder the terms: 8x = (6 + 8x)(x + -1) + 22 Reorder the terms: 8x = (6 + 8x)(-1 + x) + 22 Multiply (6 + 8x) * (-1 + x) 8x = (6(-1 + x) + 8x * (-1 + x)) + 22 8x = ((-1 * 6 + x * 6) + 8x * (-1 + x)) + 22 8x = ((-6 + 6x) + 8x * (-1 + x)) + 22 8x = (-6 + 6x + (-1 * 8x + x * 8x)) + 22 8x = (-6 + 6x + (-8x + 8x2)) + 22 Combine like terms: 6x + -8x = -2x 8x = (-6 + -2x + 8x2) + 22 Reorder the terms: 8x = -6 + 22 + -2x + 8x2 Combine like terms: -6 + 22 = 16 8x = 16 + -2x + 8x2 Solving 8x = 16 + -2x + 8x2 Solving for variable 'x'. Reorder the terms: -16 + 8x + 2x + -8x2 = 16 + -2x + 8x2 + -16 + 2x + -8x2 Combine like terms: 8x + 2x = 10x -16 + 10x + -8x2 = 16 + -2x + 8x2 + -16 + 2x + -8x2 Reorder the terms: -16 + 10x + -8x2 = 16 + -16 + -2x + 2x + 8x2 + -8x2 Combine like terms: 16 + -16 = 0 -16 + 10x + -8x2 = 0 + -2x + 2x + 8x2 + -8x2 -16 + 10x + -8x2 = -2x + 2x + 8x2 + -8x2 Combine like terms: -2x + 2x = 0 -16 + 10x + -8x2 = 0 + 8x2 + -8x2 -16 + 10x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -16 + 10x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 5x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying -8 + 5x + -4x2 = 0 Solving -8 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2 + -1.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.25x + x2 = 0 + -2 -1.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.25x + x2 = -2 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 = -2 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -2 + 0.390625 Combine like terms: -2 + 0.390625 = -1.609375 0.390625 + -1.25x + x2 = -1.609375 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -1.609375 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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