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Simplifying -16t2 + 120t + 5 = 229 Reorder the terms: 5 + 120t + -16t2 = 229 Solving 5 + 120t + -16t2 = 229 Solving for variable 't'. Reorder the terms: 5 + -229 + 120t + -16t2 = 229 + -229 Combine like terms: 5 + -229 = -224 -224 + 120t + -16t2 = 229 + -229 Combine like terms: 229 + -229 = 0 -224 + 120t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-28 + 15t + -2t2) = 0 Factor a trinomial. 8((-4 + t)(7 + -2t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-4 + t)' equal to zero and attempt to solve: Simplifying -4 + t = 0 Solving -4 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + t = 0 + 4 t = 0 + 4 Combine like terms: 0 + 4 = 4 t = 4 Simplifying t = 4Subproblem 2
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Solution
t = {4, 3.5}
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