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Simplifying -4d + 2d(3 + d) = -14 -4d + (3 * 2d + d * 2d) = -14 -4d + (6d + 2d2) = -14 Combine like terms: -4d + 6d = 2d 2d + 2d2 = -14 Solving 2d + 2d2 = -14 Solving for variable 'd'. Reorder the terms: 14 + 2d + 2d2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + 2d + 2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + d + d2)' equal to zero and attempt to solve: Simplifying 7 + d + d2 = 0 Solving 7 + d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + d + -7 + d2 = 0 + -7 Reorder the terms: 7 + -7 + d + d2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + d + d2 = 0 + -7 d + d2 = 0 + -7 Combine like terms: 0 + -7 = -7 d + d2 = -7 The d term is d. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. d + 0.25 + d2 = -7 + 0.25 Reorder the terms: 0.25 + d + d2 = -7 + 0.25 Combine like terms: -7 + 0.25 = -6.75 0.25 + d + d2 = -6.75 Factor a perfect square on the left side: (d + 0.5)(d + 0.5) = -6.75 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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