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Simplifying 850 = 32d2 + 32d Reorder the terms: 850 = 32d + 32d2 Solving 850 = 32d + 32d2 Solving for variable 'd'. Reorder the terms: 850 + -32d + -32d2 = 32d + -32d + 32d2 + -32d2 Combine like terms: 32d + -32d = 0 850 + -32d + -32d2 = 0 + 32d2 + -32d2 850 + -32d + -32d2 = 32d2 + -32d2 Combine like terms: 32d2 + -32d2 = 0 850 + -32d + -32d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(425 + -16d + -16d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(425 + -16d + -16d2)' equal to zero and attempt to solve: Simplifying 425 + -16d + -16d2 = 0 Solving 425 + -16d + -16d2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -26.5625 + d + d2 = 0 Move the constant term to the right: Add '26.5625' to each side of the equation. -26.5625 + d + 26.5625 + d2 = 0 + 26.5625 Reorder the terms: -26.5625 + 26.5625 + d + d2 = 0 + 26.5625 Combine like terms: -26.5625 + 26.5625 = 0.0000 0.0000 + d + d2 = 0 + 26.5625 d + d2 = 0 + 26.5625 Combine like terms: 0 + 26.5625 = 26.5625 d + d2 = 26.5625 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. + 0.25 + d2 = 26.5625 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + d2 = 26.5625 + 0.25 Combine like terms: 26.5625 + 0.25 = 26.8125 1.25 + d2 = 26.8125 Factor a perfect square on the left side: (d + 0.5)(d + 0.5) = 26.8125 Calculate the square root of the right side: 5.178078794 Break this problem into two subproblems by setting (d + 0.5) equal to 5.178078794 and -5.178078794.Subproblem 1
d + 0.5 = 5.178078794 Simplifying d + 0.5 = 5.178078794 Reorder the terms: 0.5 + d = 5.178078794 Solving 0.5 + d = 5.178078794 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 = 5.178078794 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = 5.178078794 + -0.5 d = 5.178078794 + -0.5 Combine like terms: 5.178078794 + -0.5 = 4.678078794 d = 4.678078794 Simplifying d = 4.678078794Subproblem 2
d + 0.5 = -5.178078794 Simplifying d + 0.5 = -5.178078794 Reorder the terms: 0.5 + d = -5.178078794 Solving 0.5 + d = -5.178078794 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 = -5.178078794 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = -5.178078794 + -0.5 d = -5.178078794 + -0.5 Combine like terms: -5.178078794 + -0.5 = -5.678078794 d = -5.678078794 Simplifying d = -5.678078794Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.678078794, -5.678078794}Solution
d = {4.678078794, -5.678078794}
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