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Simplifying 224 = 144t + -16t2 Solving 224 = 144t + -16t2 Solving for variable 't'. Reorder the terms: 224 + -144t + 16t2 = 144t + -144t + -16t2 + 16t2 Combine like terms: 144t + -144t = 0 224 + -144t + 16t2 = 0 + -16t2 + 16t2 224 + -144t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 224 + -144t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(14 + -9t + t2) = 0 Factor a trinomial. 16((2 + -1t)(7 + -1t)) = 0 Ignore the factor 16.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 '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 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 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {2, 7}
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