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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 = 37.30769231 25 + -10t + t2 = 37.30769231 Factor a perfect square on the left side: (t + -5)(t + -5) = 37.30769231 Calculate the square root of the right side: 6.108002317 Break this problem into two subproblems by setting (t + -5) equal to 6.108002317 and -6.108002317.Subproblem 1
t + -5 = 6.108002317 Simplifying t + -5 = 6.108002317 Reorder the terms: -5 + t = 6.108002317 Solving -5 + t = 6.108002317 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 = 6.108002317 + 5 Combine like terms: -5 + 5 = 0 0 + t = 6.108002317 + 5 t = 6.108002317 + 5 Combine like terms: 6.108002317 + 5 = 11.108002317 t = 11.108002317 Simplifying t = 11.108002317Subproblem 2
t + -5 = -6.108002317 Simplifying t + -5 = -6.108002317 Reorder the terms: -5 + t = -6.108002317 Solving -5 + t = -6.108002317 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 = -6.108002317 + 5 Combine like terms: -5 + 5 = 0 0 + t = -6.108002317 + 5 t = -6.108002317 + 5 Combine like terms: -6.108002317 + 5 = -1.108002317 t = -1.108002317 Simplifying t = -1.108002317Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.108002317, -1.108002317}
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