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Simplifying -2t2 + 60t = 82 Reorder the terms: 60t + -2t2 = 82 Solving 60t + -2t2 = 82 Solving for variable 't'. Reorder the terms: -82 + 60t + -2t2 = 82 + -82 Combine like terms: 82 + -82 = 0 -82 + 60t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + 30t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + 30t + -1t2)' equal to zero and attempt to solve: Simplifying -41 + 30t + -1t2 = 0 Solving -41 + 30t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 41 + -30t + t2 = 0 Move the constant term to the right: Add '-41' to each side of the equation. 41 + -30t + -41 + t2 = 0 + -41 Reorder the terms: 41 + -41 + -30t + t2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -30t + t2 = 0 + -41 -30t + t2 = 0 + -41 Combine like terms: 0 + -41 = -41 -30t + t2 = -41 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = -41 + 225 Reorder the terms: 225 + -30t + t2 = -41 + 225 Combine like terms: -41 + 225 = 184 225 + -30t + t2 = 184 Factor a perfect square on the left side: (t + -15)(t + -15) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (t + -15) equal to 13.564659966 and -13.564659966.Subproblem 1
t + -15 = 13.564659966 Simplifying t + -15 = 13.564659966 Reorder the terms: -15 + t = 13.564659966 Solving -15 + t = 13.564659966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 13.564659966 + 15 Combine like terms: -15 + 15 = 0 0 + t = 13.564659966 + 15 t = 13.564659966 + 15 Combine like terms: 13.564659966 + 15 = 28.564659966 t = 28.564659966 Simplifying t = 28.564659966Subproblem 2
t + -15 = -13.564659966 Simplifying t + -15 = -13.564659966 Reorder the terms: -15 + t = -13.564659966 Solving -15 + t = -13.564659966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -13.564659966 + 15 Combine like terms: -15 + 15 = 0 0 + t = -13.564659966 + 15 t = -13.564659966 + 15 Combine like terms: -13.564659966 + 15 = 1.435340034 t = 1.435340034 Simplifying t = 1.435340034Solution
The solution to the problem is based on the solutions from the subproblems. t = {28.564659966, 1.435340034}Solution
t = {28.564659966, 1.435340034}
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