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Simplifying 6d + -3d2 = 9 Solving 6d + -3d2 = 9 Solving for variable 'd'. Reorder the terms: -9 + 6d + -3d2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 6d + -3d2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 2d + -1d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 2d + -1d2)' equal to zero and attempt to solve: Simplifying -3 + 2d + -1d2 = 0 Solving -3 + 2d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -2d + d2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2d + -3 + d2 = 0 + -3 Reorder the terms: 3 + -3 + -2d + d2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2d + d2 = 0 + -3 -2d + d2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2d + d2 = -3 The d term is -2d. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2d + 1 + d2 = -3 + 1 Reorder the terms: 1 + -2d + d2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2d + d2 = -2 Factor a perfect square on the left side: (d + -1)(d + -1) = -2 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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