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Simplifying 7 + -4d(d + -3) = 23 Reorder the terms: 7 + -4d(-3 + d) = 23 7 + (-3 * -4d + d * -4d) = 23 7 + (12d + -4d2) = 23 Solving 7 + 12d + -4d2 = 23 Solving for variable 'd'. Reorder the terms: 7 + -23 + 12d + -4d2 = 23 + -23 Combine like terms: 7 + -23 = -16 -16 + 12d + -4d2 = 23 + -23 Combine like terms: 23 + -23 = 0 -16 + 12d + -4d2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 3d + -1d2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 3d + -1d2)' equal to zero and attempt to solve: Simplifying -4 + 3d + -1d2 = 0 Solving -4 + 3d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -3d + d2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3d + -4 + d2 = 0 + -4 Reorder the terms: 4 + -4 + -3d + d2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3d + d2 = 0 + -4 -3d + d2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3d + d2 = -4 The d term is -3d. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3d + 2.25 + d2 = -4 + 2.25 Reorder the terms: 2.25 + -3d + d2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3d + d2 = -1.75 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = -1.75 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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