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Simplifying 196 = -16t2 + 18t + 224 Reorder the terms: 196 = 224 + 18t + -16t2 Solving 196 = 224 + 18t + -16t2 Solving for variable 't'. Combine like terms: 196 + -224 = -28 -28 + -18t + 16t2 = 224 + 18t + -16t2 + -224 + -18t + 16t2 Reorder the terms: -28 + -18t + 16t2 = 224 + -224 + 18t + -18t + -16t2 + 16t2 Combine like terms: 224 + -224 = 0 -28 + -18t + 16t2 = 0 + 18t + -18t + -16t2 + 16t2 -28 + -18t + 16t2 = 18t + -18t + -16t2 + 16t2 Combine like terms: 18t + -18t = 0 -28 + -18t + 16t2 = 0 + -16t2 + 16t2 -28 + -18t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -28 + -18t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -9t + 8t2) = 0 Factor a trinomial. 2((-7 + -8t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -8t)' equal to zero and attempt to solve: Simplifying -7 + -8t = 0 Solving -7 + -8t = 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 + -8t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8t = 0 + 7 -8t = 0 + 7 Combine like terms: 0 + 7 = 7 -8t = 7 Divide each side by '-8'. t = -0.875 Simplifying t = -0.875Subproblem 2
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 = 2Solution
t = {-0.875, 2}
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