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Simplifying -13d2 + -13d + 10 = 0 Reorder the terms: 10 + -13d + -13d2 = 0 Solving 10 + -13d + -13d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.7692307692 + d + d2 = 0 Move the constant term to the right: Add '0.7692307692' to each side of the equation. -0.7692307692 + d + 0.7692307692 + d2 = 0 + 0.7692307692 Reorder the terms: -0.7692307692 + 0.7692307692 + d + d2 = 0 + 0.7692307692 Combine like terms: -0.7692307692 + 0.7692307692 = 0.0000000000 0.0000000000 + d + d2 = 0 + 0.7692307692 d + d2 = 0 + 0.7692307692 Combine like terms: 0 + 0.7692307692 = 0.7692307692 d + d2 = 0.7692307692 The d term is d. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + d2 = 0.7692307692 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + d2 = 0.7692307692 + 0.25 Combine like terms: 0.7692307692 + 0.25 = 1.0192307692 1.25 + d2 = 1.0192307692 Factor a perfect square on the left side: (d + 0.5)(d + 0.5) = 1.0192307692 Calculate the square root of the right side: 1.009569596 Break this problem into two subproblems by setting (d + 0.5) equal to 1.009569596 and -1.009569596.Subproblem 1
d + 0.5 = 1.009569596 Simplifying d + 0.5 = 1.009569596 Reorder the terms: 0.5 + d = 1.009569596 Solving 0.5 + d = 1.009569596 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + d = 1.009569596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = 1.009569596 + -0.5 d = 1.009569596 + -0.5 Combine like terms: 1.009569596 + -0.5 = 0.509569596 d = 0.509569596 Simplifying d = 0.509569596Subproblem 2
d + 0.5 = -1.009569596 Simplifying d + 0.5 = -1.009569596 Reorder the terms: 0.5 + d = -1.009569596 Solving 0.5 + d = -1.009569596 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + d = -1.009569596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = -1.009569596 + -0.5 d = -1.009569596 + -0.5 Combine like terms: -1.009569596 + -0.5 = -1.509569596 d = -1.509569596 Simplifying d = -1.509569596Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.509569596, -1.509569596}
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