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Simplifying 49t2 + 5 = 42t Reorder the terms: 5 + 49t2 = 42t Solving 5 + 49t2 = 42t Solving for variable 't'. Reorder the terms: 5 + -42t + 49t2 = 42t + -42t Combine like terms: 42t + -42t = 0 5 + -42t + 49t2 = 0 Factor a trinomial. (1 + -7t)(5 + -7t) = 0Subproblem 1
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 = 0.1428571429Subproblem 2
Set the factor '(5 + -7t)' equal to zero and attempt to solve: Simplifying 5 + -7t = 0 Solving 5 + -7t = 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 + -7t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7t = 0 + -5 -7t = 0 + -5 Combine like terms: 0 + -5 = -5 -7t = -5 Divide each side by '-7'. t = 0.7142857143 Simplifying t = 0.7142857143Solution
t = {0.1428571429, 0.7142857143}
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