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Simplifying 4d2 + -39d + 72 = 0 Reorder the terms: 72 + -39d + 4d2 = 0 Solving 72 + -39d + 4d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 18 + -9.75d + d2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -9.75d + -18 + d2 = 0 + -18 Reorder the terms: 18 + -18 + -9.75d + d2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -9.75d + d2 = 0 + -18 -9.75d + d2 = 0 + -18 Combine like terms: 0 + -18 = -18 -9.75d + d2 = -18 The d term is -9.75d. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75d + 23.765625 + d2 = -18 + 23.765625 Reorder the terms: 23.765625 + -9.75d + d2 = -18 + 23.765625 Combine like terms: -18 + 23.765625 = 5.765625 23.765625 + -9.75d + d2 = 5.765625 Factor a perfect square on the left side: (d + -4.875)(d + -4.875) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (d + -4.875) equal to 2.401171589 and -2.401171589.Subproblem 1
d + -4.875 = 2.401171589 Simplifying d + -4.875 = 2.401171589 Reorder the terms: -4.875 + d = 2.401171589 Solving -4.875 + d = 2.401171589 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + d = 2.401171589 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + d = 2.401171589 + 4.875 d = 2.401171589 + 4.875 Combine like terms: 2.401171589 + 4.875 = 7.276171589 d = 7.276171589 Simplifying d = 7.276171589Subproblem 2
d + -4.875 = -2.401171589 Simplifying d + -4.875 = -2.401171589 Reorder the terms: -4.875 + d = -2.401171589 Solving -4.875 + d = -2.401171589 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + d = -2.401171589 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + d = -2.401171589 + 4.875 d = -2.401171589 + 4.875 Combine like terms: -2.401171589 + 4.875 = 2.473828411 d = 2.473828411 Simplifying d = 2.473828411Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.276171589, 2.473828411}
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