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Simplifying -16t2 + 120t + 500 = 700 Reorder the terms: 500 + 120t + -16t2 = 700 Solving 500 + 120t + -16t2 = 700 Solving for variable 't'. Reorder the terms: 500 + -700 + 120t + -16t2 = 700 + -700 Combine like terms: 500 + -700 = -200 -200 + 120t + -16t2 = 700 + -700 Combine like terms: 700 + -700 = 0 -200 + 120t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-25 + 15t + -2t2) = 0 Factor a trinomial. 8((-5 + t)(5 + -2t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + t)' equal to zero and attempt to solve: Simplifying -5 + t = 0 Solving -5 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + t = 0 + 5 t = 0 + 5 Combine like terms: 0 + 5 = 5 t = 5 Simplifying t = 5Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {5, 2.5}
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