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Simplifying 10h(h + 4) = 450 Reorder the terms: 10h(4 + h) = 450 (4 * 10h + h * 10h) = 450 (40h + 10h2) = 450 Solving 40h + 10h2 = 450 Solving for variable 'h'. Reorder the terms: -450 + 40h + 10h2 = 450 + -450 Combine like terms: 450 + -450 = 0 -450 + 40h + 10h2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-45 + 4h + h2) = 0 Factor a trinomial. 10((-9 + -1h)(5 + -1h)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-9 + -1h)' equal to zero and attempt to solve: Simplifying -9 + -1h = 0 Solving -9 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1h = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1h = 0 + 9 -1h = 0 + 9 Combine like terms: 0 + 9 = 9 -1h = 9 Divide each side by '-1'. h = -9 Simplifying h = -9Subproblem 2
Set the factor '(5 + -1h)' equal to zero and attempt to solve: Simplifying 5 + -1h = 0 Solving 5 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1h = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1h = 0 + -5 -1h = 0 + -5 Combine like terms: 0 + -5 = -5 -1h = -5 Divide each side by '-1'. h = 5 Simplifying h = 5Solution
h = {-9, 5}
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