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Simplifying 45 = 16t2 + 25t + 45 Reorder the terms: 45 = 45 + 25t + 16t2 Add '-45' to each side of the equation. 45 + -45 = 45 + 25t + -45 + 16t2 Combine like terms: 45 + -45 = 0 0 = 45 + 25t + -45 + 16t2 Reorder the terms: 0 = 45 + -45 + 25t + 16t2 Combine like terms: 45 + -45 = 0 0 = 0 + 25t + 16t2 0 = 25t + 16t2 Solving 0 = 25t + 16t2 Solving for variable 't'. Remove the zero: -25t + -16t2 = 25t + 16t2 + -25t + -16t2 Reorder the terms: -25t + -16t2 = 25t + -25t + 16t2 + -16t2 Combine like terms: 25t + -25t = 0 -25t + -16t2 = 0 + 16t2 + -16t2 -25t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -25t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1t'. -1t(25 + 16t) = 0 Ignore the factor -1.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(25 + 16t)' equal to zero and attempt to solve: Simplifying 25 + 16t = 0 Solving 25 + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 16t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 16t = 0 + -25 16t = 0 + -25 Combine like terms: 0 + -25 = -25 16t = -25 Divide each side by '16'. t = -1.5625 Simplifying t = -1.5625Solution
t = {0, -1.5625}
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