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Simplifying 80 = 48t + -4t2 Solving 80 = 48t + -4t2 Solving for variable 't'. Reorder the terms: 80 + -48t + 4t2 = 48t + -48t + -4t2 + 4t2 Combine like terms: 48t + -48t = 0 80 + -48t + 4t2 = 0 + -4t2 + 4t2 80 + -48t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 80 + -48t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(20 + -12t + t2) = 0 Factor a trinomial. 4((2 + -1t)(10 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {2, 10}
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