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Simplifying 16t2 + -180t + 296 = 0 Reorder the terms: 296 + -180t + 16t2 = 0 Solving 296 + -180t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(74 + -45t + 4t2) = 0 Factor a trinomial. 4((2 + -1t)(37 + -4t)) = 0 Ignore the factor 4.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 '(37 + -4t)' equal to zero and attempt to solve: Simplifying 37 + -4t = 0 Solving 37 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + -4t = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -4t = 0 + -37 -4t = 0 + -37 Combine like terms: 0 + -37 = -37 -4t = -37 Divide each side by '-4'. t = 9.25 Simplifying t = 9.25Solution
t = {2, 9.25}
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