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Simplifying 7d2 = 50d + 7 Reorder the terms: 7d2 = 7 + 50d Solving 7d2 = 7 + 50d Solving for variable 'd'. Reorder the terms: -7 + -50d + 7d2 = 7 + 50d + -7 + -50d Reorder the terms: -7 + -50d + 7d2 = 7 + -7 + 50d + -50d Combine like terms: 7 + -7 = 0 -7 + -50d + 7d2 = 0 + 50d + -50d -7 + -50d + 7d2 = 50d + -50d Combine like terms: 50d + -50d = 0 -7 + -50d + 7d2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -7.142857143d + d2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -7.142857143d + 1 + d2 = 0 + 1 Reorder the terms: -1 + 1 + -7.142857143d + d2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7.142857143d + d2 = 0 + 1 -7.142857143d + d2 = 0 + 1 Combine like terms: 0 + 1 = 1 -7.142857143d + d2 = 1 The d term is -7.142857143d. Take half its coefficient (-3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. -7.142857143d + 12.75510204 + d2 = 1 + 12.75510204 Reorder the terms: 12.75510204 + -7.142857143d + d2 = 1 + 12.75510204 Combine like terms: 1 + 12.75510204 = 13.75510204 12.75510204 + -7.142857143d + d2 = 13.75510204 Factor a perfect square on the left side: (d + -3.571428572)(d + -3.571428572) = 13.75510204 Calculate the square root of the right side: 3.708787139 Break this problem into two subproblems by setting (d + -3.571428572) equal to 3.708787139 and -3.708787139.Subproblem 1
d + -3.571428572 = 3.708787139 Simplifying d + -3.571428572 = 3.708787139 Reorder the terms: -3.571428572 + d = 3.708787139 Solving -3.571428572 + d = 3.708787139 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3.571428572' to each side of the equation. -3.571428572 + 3.571428572 + d = 3.708787139 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + d = 3.708787139 + 3.571428572 d = 3.708787139 + 3.571428572 Combine like terms: 3.708787139 + 3.571428572 = 7.280215711 d = 7.280215711 Simplifying d = 7.280215711Subproblem 2
d + -3.571428572 = -3.708787139 Simplifying d + -3.571428572 = -3.708787139 Reorder the terms: -3.571428572 + d = -3.708787139 Solving -3.571428572 + d = -3.708787139 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3.571428572' to each side of the equation. -3.571428572 + 3.571428572 + d = -3.708787139 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + d = -3.708787139 + 3.571428572 d = -3.708787139 + 3.571428572 Combine like terms: -3.708787139 + 3.571428572 = -0.137358567 d = -0.137358567 Simplifying d = -0.137358567Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.280215711, -0.137358567}
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