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Simplifying 4 + -5d = 7d2 Solving 4 + -5d = 7d2 Solving for variable 'd'. Combine like terms: 7d2 + -7d2 = 0 4 + -5d + -7d2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.5714285714 + 0.7142857143d + d2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.7142857143d + 0.5714285714 + d2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.7142857143d + d2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.7142857143d + d2 = 0 + 0.5714285714 0.7142857143d + d2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.7142857143d + d2 = 0.5714285714 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 = 0.5714285714 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143d + d2 = 0.5714285714 + 0.1275510204 Combine like terms: 0.5714285714 + 0.1275510204 = 0.6989795918 0.1275510204 + 0.7142857143d + d2 = 0.6989795918 Factor a perfect square on the left side: (d + 0.3571428572)(d + 0.3571428572) = 0.6989795918 Calculate the square root of the right side: 0.836049994 Break this problem into two subproblems by setting (d + 0.3571428572) equal to 0.836049994 and -0.836049994.Subproblem 1
d + 0.3571428572 = 0.836049994 Simplifying d + 0.3571428572 = 0.836049994 Reorder the terms: 0.3571428572 + d = 0.836049994 Solving 0.3571428572 + d = 0.836049994 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 = 0.836049994 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + d = 0.836049994 + -0.3571428572 d = 0.836049994 + -0.3571428572 Combine like terms: 0.836049994 + -0.3571428572 = 0.4789071368 d = 0.4789071368 Simplifying d = 0.4789071368Subproblem 2
d + 0.3571428572 = -0.836049994 Simplifying d + 0.3571428572 = -0.836049994 Reorder the terms: 0.3571428572 + d = -0.836049994 Solving 0.3571428572 + d = -0.836049994 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 = -0.836049994 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + d = -0.836049994 + -0.3571428572 d = -0.836049994 + -0.3571428572 Combine like terms: -0.836049994 + -0.3571428572 = -1.1931928512 d = -1.1931928512 Simplifying d = -1.1931928512Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.4789071368, -1.1931928512}
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