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Simplifying 42t2 + 10t + -8 = 0 Reorder the terms: -8 + 10t + 42t2 = 0 Solving -8 + 10t + 42t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 5t + 21t2) = 0 Factor a trinomial. 2((-4 + -7t)(1 + -3t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -7t)' equal to zero and attempt to solve: Simplifying -4 + -7t = 0 Solving -4 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -7t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7t = 0 + 4 -7t = 0 + 4 Combine like terms: 0 + 4 = 4 -7t = 4 Divide each side by '-7'. t = -0.5714285714 Simplifying t = -0.5714285714Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve: Simplifying 1 + -3t = 0 Solving 1 + -3t = 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 + -3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3t = 0 + -1 -3t = 0 + -1 Combine like terms: 0 + -1 = -1 -3t = -1 Divide each side by '-3'. t = 0.3333333333 Simplifying t = 0.3333333333Solution
t = {-0.5714285714, 0.3333333333}
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