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Simplifying -4d2 + 7d + 13 = 0 Reorder the terms: 13 + 7d + -4d2 = 0 Solving 13 + 7d + -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'. -3.25 + -1.75d + d2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -1.75d + 3.25 + d2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -1.75d + d2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -1.75d + d2 = 0 + 3.25 -1.75d + d2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -1.75d + d2 = 3.25 The d term is -1.75d. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75d + 0.765625 + d2 = 3.25 + 0.765625 Reorder the terms: 0.765625 + -1.75d + d2 = 3.25 + 0.765625 Combine like terms: 3.25 + 0.765625 = 4.015625 0.765625 + -1.75d + d2 = 4.015625 Factor a perfect square on the left side: (d + -0.875)(d + -0.875) = 4.015625 Calculate the square root of the right side: 2.003902443 Break this problem into two subproblems by setting (d + -0.875) equal to 2.003902443 and -2.003902443.Subproblem 1
d + -0.875 = 2.003902443 Simplifying d + -0.875 = 2.003902443 Reorder the terms: -0.875 + d = 2.003902443 Solving -0.875 + d = 2.003902443 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + d = 2.003902443 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + d = 2.003902443 + 0.875 d = 2.003902443 + 0.875 Combine like terms: 2.003902443 + 0.875 = 2.878902443 d = 2.878902443 Simplifying d = 2.878902443Subproblem 2
d + -0.875 = -2.003902443 Simplifying d + -0.875 = -2.003902443 Reorder the terms: -0.875 + d = -2.003902443 Solving -0.875 + d = -2.003902443 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + d = -2.003902443 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + d = -2.003902443 + 0.875 d = -2.003902443 + 0.875 Combine like terms: -2.003902443 + 0.875 = -1.128902443 d = -1.128902443 Simplifying d = -1.128902443Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.878902443, -1.128902443}
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