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Simplifying d2 + -7d + -7 = 0 Reorder the terms: -7 + -7d + d2 = 0 Solving -7 + -7d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -7d + 7 + d2 = 0 + 7 Reorder the terms: -7 + 7 + -7d + d2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -7d + d2 = 0 + 7 -7d + d2 = 0 + 7 Combine like terms: 0 + 7 = 7 -7d + d2 = 7 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 = 7 + 12.25 Reorder the terms: 12.25 + -7d + d2 = 7 + 12.25 Combine like terms: 7 + 12.25 = 19.25 12.25 + -7d + d2 = 19.25 Factor a perfect square on the left side: (d + -3.5)(d + -3.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (d + -3.5) equal to 4.387482194 and -4.387482194.Subproblem 1
d + -3.5 = 4.387482194 Simplifying d + -3.5 = 4.387482194 Reorder the terms: -3.5 + d = 4.387482194 Solving -3.5 + d = 4.387482194 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 = 4.387482194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + d = 4.387482194 + 3.5 d = 4.387482194 + 3.5 Combine like terms: 4.387482194 + 3.5 = 7.887482194 d = 7.887482194 Simplifying d = 7.887482194Subproblem 2
d + -3.5 = -4.387482194 Simplifying d + -3.5 = -4.387482194 Reorder the terms: -3.5 + d = -4.387482194 Solving -3.5 + d = -4.387482194 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 = -4.387482194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + d = -4.387482194 + 3.5 d = -4.387482194 + 3.5 Combine like terms: -4.387482194 + 3.5 = -0.887482194 d = -0.887482194 Simplifying d = -0.887482194Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.887482194, -0.887482194}
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