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Simplifying 7d2 + 5d + -13 = 0 Reorder the terms: -13 + 5d + 7d2 = 0 Solving -13 + 5d + 7d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + 0.7142857143d + d2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + 0.7142857143d + 1.857142857 + d2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + 0.7142857143d + d2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + 0.7142857143d + d2 = 0 + 1.857142857 0.7142857143d + d2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 0.7142857143d + d2 = 1.857142857 The d term is 0.7142857143d. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143d + 0.1275510204 + d2 = 1.857142857 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143d + d2 = 1.857142857 + 0.1275510204 Combine like terms: 1.857142857 + 0.1275510204 = 1.9846938774 0.1275510204 + 0.7142857143d + d2 = 1.9846938774 Factor a perfect square on the left side: (d + 0.3571428572)(d + 0.3571428572) = 1.9846938774 Calculate the square root of the right side: 1.408791637 Break this problem into two subproblems by setting (d + 0.3571428572) equal to 1.408791637 and -1.408791637.Subproblem 1
d + 0.3571428572 = 1.408791637 Simplifying d + 0.3571428572 = 1.408791637 Reorder the terms: 0.3571428572 + d = 1.408791637 Solving 0.3571428572 + d = 1.408791637 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + d = 1.408791637 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + d = 1.408791637 + -0.3571428572 d = 1.408791637 + -0.3571428572 Combine like terms: 1.408791637 + -0.3571428572 = 1.0516487798 d = 1.0516487798 Simplifying d = 1.0516487798Subproblem 2
d + 0.3571428572 = -1.408791637 Simplifying d + 0.3571428572 = -1.408791637 Reorder the terms: 0.3571428572 + d = -1.408791637 Solving 0.3571428572 + d = -1.408791637 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + d = -1.408791637 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + d = -1.408791637 + -0.3571428572 d = -1.408791637 + -0.3571428572 Combine like terms: -1.408791637 + -0.3571428572 = -1.7659344942 d = -1.7659344942 Simplifying d = -1.7659344942Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.0516487798, -1.7659344942}
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