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Simplifying r2 + 5rh + -24h2 = 0 Reorder the terms: 5hr + -24h2 + r2 = 0 Solving 5hr + -24h2 + r2 = 0 Solving for variable 'h'. Factor a trinomial. (-8h + -1r)(3h + -1r) = 0Subproblem 1
Set the factor '(-8h + -1r)' equal to zero and attempt to solve: Simplifying -8h + -1r = 0 Solving -8h + -1r = 0 Move all terms containing h to the left, all other terms to the right. Add 'r' to each side of the equation. -8h + -1r + r = 0 + r Combine like terms: -1r + r = 0 -8h + 0 = 0 + r -8h = 0 + r Remove the zero: -8h = r Divide each side by '-8'. h = -0.125r Simplifying h = -0.125rSubproblem 2
Set the factor '(3h + -1r)' equal to zero and attempt to solve: Simplifying 3h + -1r = 0 Solving 3h + -1r = 0 Move all terms containing h to the left, all other terms to the right. Add 'r' to each side of the equation. 3h + -1r + r = 0 + r Combine like terms: -1r + r = 0 3h + 0 = 0 + r 3h = 0 + r Remove the zero: 3h = r Divide each side by '3'. h = 0.3333333333r Simplifying h = 0.3333333333rSolution
h = {-0.125r, 0.3333333333r}
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