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Simplifying 22t + -10 + -4t2 = 0 Reorder the terms: -10 + 22t + -4t2 = 0 Solving -10 + 22t + -4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 11t + -2t2) = 0 Factor a trinomial. 2((-5 + t)(1 + -2t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + t)' equal to zero and attempt to solve: Simplifying -5 + t = 0 Solving -5 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + t = 0 + 5 t = 0 + 5 Combine like terms: 0 + 5 = 5 t = 5 Simplifying t = 5Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 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 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Solution
t = {5, 0.5}
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