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Simplifying -4(4d2 + 3d + 2) = 0 Reorder the terms: -4(2 + 3d + 4d2) = 0 (2 * -4 + 3d * -4 + 4d2 * -4) = 0 (-8 + -12d + -16d2) = 0 Solving -8 + -12d + -16d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '-4'. -4(2 + 3d + 4d2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(2 + 3d + 4d2)' equal to zero and attempt to solve: Simplifying 2 + 3d + 4d2 = 0 Solving 2 + 3d + 4d2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 0.75d + d2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.75d + -0.5 + d2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.75d + d2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.75d + d2 = 0 + -0.5 0.75d + d2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.75d + d2 = -0.5 The d term is 0.75d. 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. 0.75d + 0.140625 + d2 = -0.5 + 0.140625 Reorder the terms: 0.140625 + 0.75d + d2 = -0.5 + 0.140625 Combine like terms: -0.5 + 0.140625 = -0.359375 0.140625 + 0.75d + d2 = -0.359375 Factor a perfect square on the left side: (d + 0.375)(d + 0.375) = -0.359375 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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