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Simplifying 16t2 + 160t + 176 = 0 Reorder the terms: 176 + 160t + 16t2 = 0 Solving 176 + 160t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(11 + 10t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(11 + 10t + t2)' equal to zero and attempt to solve: Simplifying 11 + 10t + t2 = 0 Solving 11 + 10t + t2 = 0 Begin completing the square. 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 = -1.258342613 t = -1.258342613 Simplifying t = -1.258342613Subproblem 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 = -8.741657387 t = -8.741657387 Simplifying t = -8.741657387Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.258342613, -8.741657387}Solution
t = {-1.258342613, -8.741657387}
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