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Simplifying -3t2 + 30t + -33 = 0 Reorder the terms: -33 + 30t + -3t2 = 0 Solving -33 + 30t + -3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + 10t + -1t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + 10t + -1t2)' equal to zero and attempt to solve: Simplifying -11 + 10t + -1t2 = 0 Solving -11 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -10t + t2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -10t + -11 + t2 = 0 + -11 Reorder the terms: 11 + -11 + -10t + t2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -10t + t2 = 0 + -11 -10t + t2 = 0 + -11 Combine like terms: 0 + -11 = -11 -10t + t2 = -11 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -11 + 25 Reorder the terms: 25 + -10t + t2 = -11 + 25 Combine like terms: -11 + 25 = 14 25 + -10t + t2 = 14 Factor a perfect square on the left side: (t + -5)(t + -5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (t + -5) equal to 3.741657387 and -3.741657387.Subproblem 1
t + -5 = 3.741657387 Simplifying t + -5 = 3.741657387 Reorder the terms: -5 + t = 3.741657387 Solving -5 + t = 3.741657387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.741657387 + 5 t = 3.741657387 + 5 Combine like terms: 3.741657387 + 5 = 8.741657387 t = 8.741657387 Simplifying t = 8.741657387Subproblem 2
t + -5 = -3.741657387 Simplifying t + -5 = -3.741657387 Reorder the terms: -5 + t = -3.741657387 Solving -5 + t = -3.741657387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.741657387 + 5 t = -3.741657387 + 5 Combine like terms: -3.741657387 + 5 = 1.258342613 t = 1.258342613 Simplifying t = 1.258342613Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.741657387, 1.258342613}Solution
t = {8.741657387, 1.258342613}
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