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Simplifying 4d2 + 8d = -52 Reorder the terms: 8d + 4d2 = -52 Solving 8d + 4d2 = -52 Solving for variable 'd'. Reorder the terms: 52 + 8d + 4d2 = -52 + 52 Combine like terms: -52 + 52 = 0 52 + 8d + 4d2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(13 + 2d + d2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(13 + 2d + d2)' equal to zero and attempt to solve: Simplifying 13 + 2d + d2 = 0 Solving 13 + 2d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 2d + -13 + d2 = 0 + -13 Reorder the terms: 13 + -13 + 2d + d2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2d + d2 = 0 + -13 2d + d2 = 0 + -13 Combine like terms: 0 + -13 = -13 2d + d2 = -13 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 = -13 + 1 Reorder the terms: 1 + 2d + d2 = -13 + 1 Combine like terms: -13 + 1 = -12 1 + 2d + d2 = -12 Factor a perfect square on the left side: (d + 1)(d + 1) = -12 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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