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Simplifying 5(4 + 2x)(-8x + -12) = 68 Reorder the terms: 5(4 + 2x)(-12 + -8x) = 68 Multiply (4 + 2x) * (-12 + -8x) 5(4(-12 + -8x) + 2x * (-12 + -8x)) = 68 5((-12 * 4 + -8x * 4) + 2x * (-12 + -8x)) = 68 5((-48 + -32x) + 2x * (-12 + -8x)) = 68 5(-48 + -32x + (-12 * 2x + -8x * 2x)) = 68 5(-48 + -32x + (-24x + -16x2)) = 68 Combine like terms: -32x + -24x = -56x 5(-48 + -56x + -16x2) = 68 (-48 * 5 + -56x * 5 + -16x2 * 5) = 68 (-240 + -280x + -80x2) = 68 Solving -240 + -280x + -80x2 = 68 Solving for variable 'x'. Reorder the terms: -240 + -68 + -280x + -80x2 = 68 + -68 Combine like terms: -240 + -68 = -308 -308 + -280x + -80x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -308 + -280x + -80x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(77 + 70x + 20x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(77 + 70x + 20x2)' equal to zero and attempt to solve: Simplifying 77 + 70x + 20x2 = 0 Solving 77 + 70x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 3.85 + 3.5x + x2 = 0.0 Move the constant term to the right: Add '-3.85' to each side of the equation. 3.85 + 3.5x + -3.85 + x2 = 0.0 + -3.85 Reorder the terms: 3.85 + -3.85 + 3.5x + x2 = 0.0 + -3.85 Combine like terms: 3.85 + -3.85 = 0.00 0.00 + 3.5x + x2 = 0.0 + -3.85 3.5x + x2 = 0.0 + -3.85 Combine like terms: 0.0 + -3.85 = -3.85 3.5x + x2 = -3.85 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -3.85 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -3.85 + 3.0625 Combine like terms: -3.85 + 3.0625 = -0.7875 3.0625 + 3.5x + x2 = -0.7875 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -0.7875 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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