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Simplifying 6t2 + 1 = 2t + 5t2 Reorder the terms: 1 + 6t2 = 2t + 5t2 Solving 1 + 6t2 = 2t + 5t2 Solving for variable 't'. Reorder the terms: 1 + -2t + 6t2 + -5t2 = 2t + 5t2 + -2t + -5t2 Combine like terms: 6t2 + -5t2 = 1t2 1 + -2t + 1t2 = 2t + 5t2 + -2t + -5t2 Reorder the terms: 1 + -2t + 1t2 = 2t + -2t + 5t2 + -5t2 Combine like terms: 2t + -2t = 0 1 + -2t + 1t2 = 0 + 5t2 + -5t2 1 + -2t + 1t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 1 + -2t + 1t2 = 0 Factor a trinomial. (1 + -1t)(1 + -1t) = 0Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {1, 1}
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