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Simplifying 8H2 + -24H + -80 = 0 Reorder the terms: -80 + -24H + 8H2 = 0 Solving -80 + -24H + 8H2 = 0 Solving for variable 'H'. Factor out the Greatest Common Factor (GCF), '8'. 8(-10 + -3H + H2) = 0 Factor a trinomial. 8((-2 + -1H)(5 + -1H)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + -1H)' equal to zero and attempt to solve: Simplifying -2 + -1H = 0 Solving -2 + -1H = 0 Move all terms containing H to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1H = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1H = 0 + 2 -1H = 0 + 2 Combine like terms: 0 + 2 = 2 -1H = 2 Divide each side by '-1'. H = -2 Simplifying H = -2Subproblem 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 = {-2, 5}
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