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Simplifying 4(-2d) + -12d(d + 3) = 8(-2d + 4) Remove parenthesis around (-2d) 4 * -2d + -12d(d + 3) = 8(-2d + 4) Multiply 4 * -2 -8d + -12d(d + 3) = 8(-2d + 4) Reorder the terms: -8d + -12d(3 + d) = 8(-2d + 4) -8d + (3 * -12d + d * -12d) = 8(-2d + 4) -8d + (-36d + -12d2) = 8(-2d + 4) Combine like terms: -8d + -36d = -44d -44d + -12d2 = 8(-2d + 4) Reorder the terms: -44d + -12d2 = 8(4 + -2d) -44d + -12d2 = (4 * 8 + -2d * 8) -44d + -12d2 = (32 + -16d) Solving -44d + -12d2 = 32 + -16d Solving for variable 'd'. Reorder the terms: -32 + -44d + 16d + -12d2 = 32 + -16d + -32 + 16d Combine like terms: -44d + 16d = -28d -32 + -28d + -12d2 = 32 + -16d + -32 + 16d Reorder the terms: -32 + -28d + -12d2 = 32 + -32 + -16d + 16d Combine like terms: 32 + -32 = 0 -32 + -28d + -12d2 = 0 + -16d + 16d -32 + -28d + -12d2 = -16d + 16d Combine like terms: -16d + 16d = 0 -32 + -28d + -12d2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(8 + 7d + 3d2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(8 + 7d + 3d2)' equal to zero and attempt to solve: Simplifying 8 + 7d + 3d2 = 0 Solving 8 + 7d + 3d2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 2.333333333d + d2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 2.333333333d + -2.666666667 + d2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 2.333333333d + d2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 2.333333333d + d2 = 0 + -2.666666667 2.333333333d + d2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 2.333333333d + d2 = -2.666666667 The d term is 2.333333333d. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333d + 1.361111112 + d2 = -2.666666667 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333d + d2 = -2.666666667 + 1.361111112 Combine like terms: -2.666666667 + 1.361111112 = -1.305555555 1.361111112 + 2.333333333d + d2 = -1.305555555 Factor a perfect square on the left side: (d + 1.166666667)(d + 1.166666667) = -1.305555555 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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