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Simplifying (3t + -5)(3t + -5) + 55t = 31 Reorder the terms: (-5 + 3t)(3t + -5) + 55t = 31 Reorder the terms: (-5 + 3t)(-5 + 3t) + 55t = 31 Multiply (-5 + 3t) * (-5 + 3t) (-5(-5 + 3t) + 3t * (-5 + 3t)) + 55t = 31 ((-5 * -5 + 3t * -5) + 3t * (-5 + 3t)) + 55t = 31 ((25 + -15t) + 3t * (-5 + 3t)) + 55t = 31 (25 + -15t + (-5 * 3t + 3t * 3t)) + 55t = 31 (25 + -15t + (-15t + 9t2)) + 55t = 31 Combine like terms: -15t + -15t = -30t (25 + -30t + 9t2) + 55t = 31 Reorder the terms: 25 + -30t + 55t + 9t2 = 31 Combine like terms: -30t + 55t = 25t 25 + 25t + 9t2 = 31 Solving 25 + 25t + 9t2 = 31 Solving for variable 't'. Reorder the terms: 25 + -31 + 25t + 9t2 = 31 + -31 Combine like terms: 25 + -31 = -6 -6 + 25t + 9t2 = 31 + -31 Combine like terms: 31 + -31 = 0 -6 + 25t + 9t2 = 0 Factor a trinomial. (-3 + -1t)(2 + -9t) = 0Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 2
Set the factor '(2 + -9t)' equal to zero and attempt to solve: Simplifying 2 + -9t = 0 Solving 2 + -9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -9t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9t = 0 + -2 -9t = 0 + -2 Combine like terms: 0 + -2 = -2 -9t = -2 Divide each side by '-9'. t = 0.2222222222 Simplifying t = 0.2222222222Solution
t = {-3, 0.2222222222}
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