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Simplifying -16t2 + -23t + 130 = 0 Reorder the terms: 130 + -23t + -16t2 = 0 Solving 130 + -23t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -8.125 + 1.4375t + t2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + 1.4375t + 8.125 + t2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + 1.4375t + t2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + 1.4375t + t2 = 0 + 8.125 1.4375t + t2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 1.4375t + t2 = 8.125 The t term is 1.4375t. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375t + 0.5166015625 + t2 = 8.125 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375t + t2 = 8.125 + 0.5166015625 Combine like terms: 8.125 + 0.5166015625 = 8.6416015625 0.5166015625 + 1.4375t + t2 = 8.6416015625 Factor a perfect square on the left side: (t + 0.71875)(t + 0.71875) = 8.6416015625 Calculate the square root of the right side: 2.93966011 Break this problem into two subproblems by setting (t + 0.71875) equal to 2.93966011 and -2.93966011.Subproblem 1
t + 0.71875 = 2.93966011 Simplifying t + 0.71875 = 2.93966011 Reorder the terms: 0.71875 + t = 2.93966011 Solving 0.71875 + t = 2.93966011 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + t = 2.93966011 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + t = 2.93966011 + -0.71875 t = 2.93966011 + -0.71875 Combine like terms: 2.93966011 + -0.71875 = 2.22091011 t = 2.22091011 Simplifying t = 2.22091011Subproblem 2
t + 0.71875 = -2.93966011 Simplifying t + 0.71875 = -2.93966011 Reorder the terms: 0.71875 + t = -2.93966011 Solving 0.71875 + t = -2.93966011 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + t = -2.93966011 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + t = -2.93966011 + -0.71875 t = -2.93966011 + -0.71875 Combine like terms: -2.93966011 + -0.71875 = -3.65841011 t = -3.65841011 Simplifying t = -3.65841011Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.22091011, -3.65841011}
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