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Simplifying (2h + 5) * h = 52 Reorder the terms: (5 + 2h) * h = 52 Reorder the terms for easier multiplication: h(5 + 2h) = 52 (5 * h + 2h * h) = 52 (5h + 2h2) = 52 Solving 5h + 2h2 = 52 Solving for variable 'h'. Reorder the terms: -52 + 5h + 2h2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 5h + 2h2 = 0 Factor a trinomial. (-13 + -2h)(4 + -1h) = 0Subproblem 1
Set the factor '(-13 + -2h)' equal to zero and attempt to solve: Simplifying -13 + -2h = 0 Solving -13 + -2h = 0 Move all terms containing h to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2h = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2h = 0 + 13 -2h = 0 + 13 Combine like terms: 0 + 13 = 13 -2h = 13 Divide each side by '-2'. h = -6.5 Simplifying h = -6.5Subproblem 2
Set the factor '(4 + -1h)' equal to zero and attempt to solve: Simplifying 4 + -1h = 0 Solving 4 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1h = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1h = 0 + -4 -1h = 0 + -4 Combine like terms: 0 + -4 = -4 -1h = -4 Divide each side by '-1'. h = 4 Simplifying h = 4Solution
h = {-6.5, 4}
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