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Simplifying -49t2 + 189t + 28 = 0 Reorder the terms: 28 + 189t + -49t2 = 0 Solving 28 + 189t + -49t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '7'. 7(4 + 27t + -7t2) = 0 Factor a trinomial. 7((4 + -1t)(1 + 7t)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 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 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Subproblem 2
Set the factor '(1 + 7t)' equal to zero and attempt to solve: Simplifying 1 + 7t = 0 Solving 1 + 7t = 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 + 7t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7t = 0 + -1 7t = 0 + -1 Combine like terms: 0 + -1 = -1 7t = -1 Divide each side by '7'. t = -0.1428571429 Simplifying t = -0.1428571429Solution
t = {4, -0.1428571429}
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