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Simplifying 13t2 + 130t + -117 = 0 Reorder the terms: -117 + 130t + 13t2 = 0 Solving -117 + 130t + 13t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '13'. 13(-9 + 10t + t2) = 0 Ignore the factor 13.Subproblem 1
Set the factor '(-9 + 10t + t2)' equal to zero and attempt to solve: Simplifying -9 + 10t + t2 = 0 Solving -9 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + 10t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10t + t2 = 0 + 9 10t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 10t + t2 = 9 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 = 9 + 25 Reorder the terms: 25 + 10t + t2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10t + t2 = 34 Factor a perfect square on the left side: (t + 5)(t + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (t + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
t + 5 = 5.830951895 Simplifying t + 5 = 5.830951895 Reorder the terms: 5 + t = 5.830951895 Solving 5 + t = 5.830951895 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 = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + t = 5.830951895 + -5 t = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 t = 0.830951895 Simplifying t = 0.830951895Subproblem 2
t + 5 = -5.830951895 Simplifying t + 5 = -5.830951895 Reorder the terms: 5 + t = -5.830951895 Solving 5 + t = -5.830951895 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 = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + t = -5.830951895 + -5 t = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 t = -10.830951895 Simplifying t = -10.830951895Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.830951895, -10.830951895}Solution
t = {0.830951895, -10.830951895}
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