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Simplifying -16t2 + 84t + 100 = 0 Reorder the terms: 100 + 84t + -16t2 = 0 Solving 100 + 84t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 21t + -4t2) = 0 Factor a trinomial. 4((25 + -4t)(1 + t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + -4t)' equal to zero and attempt to solve: Simplifying 25 + -4t = 0 Solving 25 + -4t = 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 + -4t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -4t = 0 + -25 -4t = 0 + -25 Combine like terms: 0 + -25 = -25 -4t = -25 Divide each side by '-4'. t = 6.25 Simplifying t = 6.25Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {6.25, -1}
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