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Simplifying -16t2 + 108t + 520 = 0 Reorder the terms: 520 + 108t + -16t2 = 0 Solving 520 + 108t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(130 + 27t + -4t2) = 0 Factor a trinomial. 4((10 + -1t)(13 + 4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Subproblem 2
Set the factor '(13 + 4t)' equal to zero and attempt to solve: Simplifying 13 + 4t = 0 Solving 13 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 4t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 4t = 0 + -13 4t = 0 + -13 Combine like terms: 0 + -13 = -13 4t = -13 Divide each side by '4'. t = -3.25 Simplifying t = -3.25Solution
t = {10, -3.25}
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