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Simplifying 13t2 + -130t + 160 = 0 Reorder the terms: 160 + -130t + 13t2 = 0 Solving 160 + -130t + 13t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 12.30769231 + -10t + t2 = 0 Move the constant term to the right: Add '-12.30769231' to each side of the equation. 12.30769231 + -10t + -12.30769231 + t2 = 0 + -12.30769231 Reorder the terms: 12.30769231 + -12.30769231 + -10t + t2 = 0 + -12.30769231 Combine like terms: 12.30769231 + -12.30769231 = 0.00000000 0.00000000 + -10t + t2 = 0 + -12.30769231 -10t + t2 = 0 + -12.30769231 Combine like terms: 0 + -12.30769231 = -12.30769231 -10t + t2 = -12.30769231 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 = -12.30769231 + 25 Reorder the terms: 25 + -10t + t2 = -12.30769231 + 25 Combine like terms: -12.30769231 + 25 = 12.69230769 25 + -10t + t2 = 12.69230769 Factor a perfect square on the left side: (t + -5)(t + -5) = 12.69230769 Calculate the square root of the right side: 3.562626516 Break this problem into two subproblems by setting (t + -5) equal to 3.562626516 and -3.562626516.Subproblem 1
t + -5 = 3.562626516 Simplifying t + -5 = 3.562626516 Reorder the terms: -5 + t = 3.562626516 Solving -5 + t = 3.562626516 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 = 3.562626516 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.562626516 + 5 t = 3.562626516 + 5 Combine like terms: 3.562626516 + 5 = 8.562626516 t = 8.562626516 Simplifying t = 8.562626516Subproblem 2
t + -5 = -3.562626516 Simplifying t + -5 = -3.562626516 Reorder the terms: -5 + t = -3.562626516 Solving -5 + t = -3.562626516 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 = -3.562626516 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.562626516 + 5 t = -3.562626516 + 5 Combine like terms: -3.562626516 + 5 = 1.437373484 t = 1.437373484 Simplifying t = 1.437373484Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.562626516, 1.437373484}
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