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Simplifying 7d = -1d2 + -2 Reorder the terms: 7d = -2 + -1d2 Solving 7d = -2 + -1d2 Solving for variable 'd'. Reorder the terms: 2 + 7d + d2 = -2 + -1d2 + 2 + d2 Reorder the terms: 2 + 7d + d2 = -2 + 2 + -1d2 + d2 Combine like terms: -2 + 2 = 0 2 + 7d + d2 = 0 + -1d2 + d2 2 + 7d + d2 = -1d2 + d2 Combine like terms: -1d2 + d2 = 0 2 + 7d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 7d + -2 + d2 = 0 + -2 Reorder the terms: 2 + -2 + 7d + d2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7d + d2 = 0 + -2 7d + d2 = 0 + -2 Combine like terms: 0 + -2 = -2 7d + d2 = -2 The d term is 7d. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7d + 12.25 + d2 = -2 + 12.25 Reorder the terms: 12.25 + 7d + d2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + 7d + d2 = 10.25 Factor a perfect square on the left side: (d + 3.5)(d + 3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (d + 3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
d + 3.5 = 3.201562119 Simplifying d + 3.5 = 3.201562119 Reorder the terms: 3.5 + d = 3.201562119 Solving 3.5 + d = 3.201562119 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = 3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = 3.201562119 + -3.5 d = 3.201562119 + -3.5 Combine like terms: 3.201562119 + -3.5 = -0.298437881 d = -0.298437881 Simplifying d = -0.298437881Subproblem 2
d + 3.5 = -3.201562119 Simplifying d + 3.5 = -3.201562119 Reorder the terms: 3.5 + d = -3.201562119 Solving 3.5 + d = -3.201562119 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = -3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = -3.201562119 + -3.5 d = -3.201562119 + -3.5 Combine like terms: -3.201562119 + -3.5 = -6.701562119 d = -6.701562119 Simplifying d = -6.701562119Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.298437881, -6.701562119}
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