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Simplifying 388 = -16t2 + 176t + 4 Reorder the terms: 388 = 4 + 176t + -16t2 Solving 388 = 4 + 176t + -16t2 Solving for variable 't'. Combine like terms: 388 + -4 = 384 384 + -176t + 16t2 = 4 + 176t + -16t2 + -4 + -176t + 16t2 Reorder the terms: 384 + -176t + 16t2 = 4 + -4 + 176t + -176t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 384 + -176t + 16t2 = 0 + 176t + -176t + -16t2 + 16t2 384 + -176t + 16t2 = 176t + -176t + -16t2 + 16t2 Combine like terms: 176t + -176t = 0 384 + -176t + 16t2 = 0 + -16t2 + 16t2 384 + -176t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 384 + -176t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(24 + -11t + t2) = 0 Factor a trinomial. 16((3 + -1t)(8 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {3, 8}
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