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Simplifying 16t2 + 38t + 1.5 = 0 Reorder the terms: 1.5 + 38t + 16t2 = 0 Solving 1.5 + 38t + 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'. 0.09375 + 2.375t + t2 = 0 Move the constant term to the right: Add '-0.09375' to each side of the equation. 0.09375 + 2.375t + -0.09375 + t2 = 0 + -0.09375 Reorder the terms: 0.09375 + -0.09375 + 2.375t + t2 = 0 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + 2.375t + t2 = 0 + -0.09375 2.375t + t2 = 0 + -0.09375 Combine like terms: 0 + -0.09375 = -0.09375 2.375t + t2 = -0.09375 The t term is 2.375t. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375t + 1.41015625 + t2 = -0.09375 + 1.41015625 Reorder the terms: 1.41015625 + 2.375t + t2 = -0.09375 + 1.41015625 Combine like terms: -0.09375 + 1.41015625 = 1.31640625 1.41015625 + 2.375t + t2 = 1.31640625 Factor a perfect square on the left side: (t + 1.1875)(t + 1.1875) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (t + 1.1875) equal to 1.147347484 and -1.147347484.Subproblem 1
t + 1.1875 = 1.147347484 Simplifying t + 1.1875 = 1.147347484 Reorder the terms: 1.1875 + t = 1.147347484 Solving 1.1875 + t = 1.147347484 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = 1.147347484 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = 1.147347484 + -1.1875 t = 1.147347484 + -1.1875 Combine like terms: 1.147347484 + -1.1875 = -0.040152516 t = -0.040152516 Simplifying t = -0.040152516Subproblem 2
t + 1.1875 = -1.147347484 Simplifying t + 1.1875 = -1.147347484 Reorder the terms: 1.1875 + t = -1.147347484 Solving 1.1875 + t = -1.147347484 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = -1.147347484 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = -1.147347484 + -1.1875 t = -1.147347484 + -1.1875 Combine like terms: -1.147347484 + -1.1875 = -2.334847484 t = -2.334847484 Simplifying t = -2.334847484Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.040152516, -2.334847484}
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