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Simplifying 4d2 + 104d = 116 Reorder the terms: 104d + 4d2 = 116 Solving 104d + 4d2 = 116 Solving for variable 'd'. Reorder the terms: -116 + 104d + 4d2 = 116 + -116 Combine like terms: 116 + -116 = 0 -116 + 104d + 4d2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-29 + 26d + d2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-29 + 26d + d2)' equal to zero and attempt to solve: Simplifying -29 + 26d + d2 = 0 Solving -29 + 26d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 26d + 29 + d2 = 0 + 29 Reorder the terms: -29 + 29 + 26d + d2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 26d + d2 = 0 + 29 26d + d2 = 0 + 29 Combine like terms: 0 + 29 = 29 26d + d2 = 29 The d term is 26d. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26d + 169 + d2 = 29 + 169 Reorder the terms: 169 + 26d + d2 = 29 + 169 Combine like terms: 29 + 169 = 198 169 + 26d + d2 = 198 Factor a perfect square on the left side: (d + 13)(d + 13) = 198 Calculate the square root of the right side: 14.071247279 Break this problem into two subproblems by setting (d + 13) equal to 14.071247279 and -14.071247279.Subproblem 1
d + 13 = 14.071247279 Simplifying d + 13 = 14.071247279 Reorder the terms: 13 + d = 14.071247279 Solving 13 + d = 14.071247279 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + d = 14.071247279 + -13 Combine like terms: 13 + -13 = 0 0 + d = 14.071247279 + -13 d = 14.071247279 + -13 Combine like terms: 14.071247279 + -13 = 1.071247279 d = 1.071247279 Simplifying d = 1.071247279Subproblem 2
d + 13 = -14.071247279 Simplifying d + 13 = -14.071247279 Reorder the terms: 13 + d = -14.071247279 Solving 13 + d = -14.071247279 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + d = -14.071247279 + -13 Combine like terms: 13 + -13 = 0 0 + d = -14.071247279 + -13 d = -14.071247279 + -13 Combine like terms: -14.071247279 + -13 = -27.071247279 d = -27.071247279 Simplifying d = -27.071247279Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.071247279, -27.071247279}Solution
d = {1.071247279, -27.071247279}
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