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Simplifying 20d2 + -60d + 50 = 0 Reorder the terms: 50 + -60d + 20d2 = 0 Solving 50 + -60d + 20d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '10'. 10(5 + -6d + 2d2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(5 + -6d + 2d2)' equal to zero and attempt to solve: Simplifying 5 + -6d + 2d2 = 0 Solving 5 + -6d + 2d2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -3d + d2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -3d + -2.5 + d2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -3d + d2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -3d + d2 = 0 + -2.5 -3d + d2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -3d + d2 = -2.5 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 = -2.5 + 2.25 Reorder the terms: 2.25 + -3d + d2 = -2.5 + 2.25 Combine like terms: -2.5 + 2.25 = -0.25 2.25 + -3d + d2 = -0.25 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = -0.25 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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