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Simplifying -169 + d2 + (d + -7) = 0 Reorder the terms: -169 + d2 + (-7 + d) = 0 Remove parenthesis around (-7 + d) -169 + d2 + -7 + d = 0 Reorder the terms: -169 + -7 + d + d2 = 0 Combine like terms: -169 + -7 = -176 -176 + d + d2 = 0 Solving -176 + d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '176' to each side of the equation. -176 + d + 176 + d2 = 0 + 176 Reorder the terms: -176 + 176 + d + d2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + d + d2 = 0 + 176 d + d2 = 0 + 176 Combine like terms: 0 + 176 = 176 d + d2 = 176 The d term is d. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. d + 0.25 + d2 = 176 + 0.25 Reorder the terms: 0.25 + d + d2 = 176 + 0.25 Combine like terms: 176 + 0.25 = 176.25 0.25 + d + d2 = 176.25 Factor a perfect square on the left side: (d + 0.5)(d + 0.5) = 176.25 Calculate the square root of the right side: 13.275918047 Break this problem into two subproblems by setting (d + 0.5) equal to 13.275918047 and -13.275918047.Subproblem 1
d + 0.5 = 13.275918047 Simplifying d + 0.5 = 13.275918047 Reorder the terms: 0.5 + d = 13.275918047 Solving 0.5 + d = 13.275918047 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + d = 13.275918047 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = 13.275918047 + -0.5 d = 13.275918047 + -0.5 Combine like terms: 13.275918047 + -0.5 = 12.775918047 d = 12.775918047 Simplifying d = 12.775918047Subproblem 2
d + 0.5 = -13.275918047 Simplifying d + 0.5 = -13.275918047 Reorder the terms: 0.5 + d = -13.275918047 Solving 0.5 + d = -13.275918047 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + d = -13.275918047 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = -13.275918047 + -0.5 d = -13.275918047 + -0.5 Combine like terms: -13.275918047 + -0.5 = -13.775918047 d = -13.775918047 Simplifying d = -13.775918047Solution
The solution to the problem is based on the solutions from the subproblems. d = {12.775918047, -13.775918047}
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