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Simplifying d2 + 28d = -33 Reorder the terms: 28d + d2 = -33 Solving 28d + d2 = -33 Solving for variable 'd'. Reorder the terms: 33 + 28d + d2 = -33 + 33 Combine like terms: -33 + 33 = 0 33 + 28d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 28d + -33 + d2 = 0 + -33 Reorder the terms: 33 + -33 + 28d + d2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 28d + d2 = 0 + -33 28d + d2 = 0 + -33 Combine like terms: 0 + -33 = -33 28d + d2 = -33 The d term is 28d. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28d + 196 + d2 = -33 + 196 Reorder the terms: 196 + 28d + d2 = -33 + 196 Combine like terms: -33 + 196 = 163 196 + 28d + d2 = 163 Factor a perfect square on the left side: (d + 14)(d + 14) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (d + 14) equal to 12.767145335 and -12.767145335.Subproblem 1
d + 14 = 12.767145335 Simplifying d + 14 = 12.767145335 Reorder the terms: 14 + d = 12.767145335 Solving 14 + d = 12.767145335 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + d = 12.767145335 + -14 Combine like terms: 14 + -14 = 0 0 + d = 12.767145335 + -14 d = 12.767145335 + -14 Combine like terms: 12.767145335 + -14 = -1.232854665 d = -1.232854665 Simplifying d = -1.232854665Subproblem 2
d + 14 = -12.767145335 Simplifying d + 14 = -12.767145335 Reorder the terms: 14 + d = -12.767145335 Solving 14 + d = -12.767145335 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + d = -12.767145335 + -14 Combine like terms: 14 + -14 = 0 0 + d = -12.767145335 + -14 d = -12.767145335 + -14 Combine like terms: -12.767145335 + -14 = -26.767145335 d = -26.767145335 Simplifying d = -26.767145335Solution
The solution to the problem is based on the solutions from the subproblems. d = {-1.232854665, -26.767145335}
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