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Simplifying h(d) = -1d2 + 50d Multiply h * d dh = -1d2 + 50d Reorder the terms: dh = 50d + -1d2 Solving dh = 50d + -1d2 Solving for variable 'd'. Reorder the terms: -50d + dh + d2 = 50d + -1d2 + -50d + d2 Reorder the terms: -50d + dh + d2 = 50d + -50d + -1d2 + d2 Combine like terms: 50d + -50d = 0 -50d + dh + d2 = 0 + -1d2 + d2 -50d + dh + d2 = -1d2 + d2 Combine like terms: -1d2 + d2 = 0 -50d + dh + d2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-50 + h + d) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-50 + h + d)' equal to zero and attempt to solve: Simplifying -50 + h + d = 0 Reorder the terms: -50 + d + h = 0 Solving -50 + d + h = 0 Move all terms containing d to the left, all other terms to the right. Add '50' to each side of the equation. -50 + d + 50 + h = 0 + 50 Reorder the terms: -50 + 50 + d + h = 0 + 50 Combine like terms: -50 + 50 = 0 0 + d + h = 0 + 50 d + h = 0 + 50 Combine like terms: 0 + 50 = 50 d + h = 50 Add '-1h' to each side of the equation. d + h + -1h = 50 + -1h Combine like terms: h + -1h = 0 d + 0 = 50 + -1h d = 50 + -1h Simplifying d = 50 + -1hSolution
d = {0, 50 + -1h}
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