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Simplifying 30d * 30d + 34d + 8 = 0 Reorder the terms for easier multiplication: 30 * 30d * d + 34d + 8 = 0 Multiply 30 * 30 900d * d + 34d + 8 = 0 Multiply d * d 900d2 + 34d + 8 = 0 Reorder the terms: 8 + 34d + 900d2 = 0 Solving 8 + 34d + 900d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 17d + 450d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 17d + 450d2)' equal to zero and attempt to solve: Simplifying 4 + 17d + 450d2 = 0 Solving 4 + 17d + 450d2 = 0 Begin completing the square. Divide all terms by 450 the coefficient of the squared term: Divide each side by '450'. 0.008888888889 + 0.03777777778d + d2 = 0.0 Move the constant term to the right: Add '-0.008888888889' to each side of the equation. 0.008888888889 + 0.03777777778d + -0.008888888889 + d2 = 0.0 + -0.008888888889 Reorder the terms: 0.008888888889 + -0.008888888889 + 0.03777777778d + d2 = 0.0 + -0.008888888889 Combine like terms: 0.008888888889 + -0.008888888889 = 0.000000000000 0.000000000000 + 0.03777777778d + d2 = 0.0 + -0.008888888889 0.03777777778d + d2 = 0.0 + -0.008888888889 Combine like terms: 0.0 + -0.008888888889 = -0.008888888889 0.03777777778d + d2 = -0.008888888889 The d term is 0.03777777778d. Take half its coefficient (0.01888888889). Square it (0.0003567901235) and add it to both sides. Add '0.0003567901235' to each side of the equation. 0.03777777778d + 0.0003567901235 + d2 = -0.008888888889 + 0.0003567901235 Reorder the terms: 0.0003567901235 + 0.03777777778d + d2 = -0.008888888889 + 0.0003567901235 Combine like terms: -0.008888888889 + 0.0003567901235 = -0.0085320987655 0.0003567901235 + 0.03777777778d + d2 = -0.0085320987655 Factor a perfect square on the left side: (d + 0.01888888889)(d + 0.01888888889) = -0.0085320987655 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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