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Simplifying 288 = 16t2 + 90t + 288 Reorder the terms: 288 = 288 + 90t + 16t2 Add '-288' to each side of the equation. 288 + -288 = 288 + 90t + -288 + 16t2 Combine like terms: 288 + -288 = 0 0 = 288 + 90t + -288 + 16t2 Reorder the terms: 0 = 288 + -288 + 90t + 16t2 Combine like terms: 288 + -288 = 0 0 = 0 + 90t + 16t2 0 = 90t + 16t2 Solving 0 = 90t + 16t2 Solving for variable 't'. Remove the zero: -90t + -16t2 = 90t + 16t2 + -90t + -16t2 Reorder the terms: -90t + -16t2 = 90t + -90t + 16t2 + -16t2 Combine like terms: 90t + -90t = 0 -90t + -16t2 = 0 + 16t2 + -16t2 -90t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -90t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2t'. -2t(45 + 8t) = 0 Ignore the factor -2.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 '(45 + 8t)' equal to zero and attempt to solve: Simplifying 45 + 8t = 0 Solving 45 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + 8t = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 8t = 0 + -45 8t = 0 + -45 Combine like terms: 0 + -45 = -45 8t = -45 Divide each side by '8'. t = -5.625 Simplifying t = -5.625Solution
t = {0, -5.625}
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