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Simplifying (3 + -2x)(-5 + 4x) = 48 + 64x Multiply (3 + -2x) * (-5 + 4x) (3(-5 + 4x) + -2x * (-5 + 4x)) = 48 + 64x ((-5 * 3 + 4x * 3) + -2x * (-5 + 4x)) = 48 + 64x ((-15 + 12x) + -2x * (-5 + 4x)) = 48 + 64x (-15 + 12x + (-5 * -2x + 4x * -2x)) = 48 + 64x (-15 + 12x + (10x + -8x2)) = 48 + 64x Combine like terms: 12x + 10x = 22x (-15 + 22x + -8x2) = 48 + 64x Solving -15 + 22x + -8x2 = 48 + 64x Solving for variable 'x'. Reorder the terms: -15 + -48 + 22x + -64x + -8x2 = 48 + 64x + -48 + -64x Combine like terms: -15 + -48 = -63 -63 + 22x + -64x + -8x2 = 48 + 64x + -48 + -64x Combine like terms: 22x + -64x = -42x -63 + -42x + -8x2 = 48 + 64x + -48 + -64x Reorder the terms: -63 + -42x + -8x2 = 48 + -48 + 64x + -64x Combine like terms: 48 + -48 = 0 -63 + -42x + -8x2 = 0 + 64x + -64x -63 + -42x + -8x2 = 64x + -64x Combine like terms: 64x + -64x = 0 -63 + -42x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(63 + 42x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(63 + 42x + 8x2)' equal to zero and attempt to solve: Simplifying 63 + 42x + 8x2 = 0 Solving 63 + 42x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 7.875 + 5.25x + x2 = 0 Move the constant term to the right: Add '-7.875' to each side of the equation. 7.875 + 5.25x + -7.875 + x2 = 0 + -7.875 Reorder the terms: 7.875 + -7.875 + 5.25x + x2 = 0 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + 5.25x + x2 = 0 + -7.875 5.25x + x2 = 0 + -7.875 Combine like terms: 0 + -7.875 = -7.875 5.25x + x2 = -7.875 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = -7.875 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -7.875 + 6.890625 Combine like terms: -7.875 + 6.890625 = -0.984375 6.890625 + 5.25x + x2 = -0.984375 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = -0.984375 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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