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Simplifying 0 = -16t2 + 9t + 41 Reorder the terms: 0 = 41 + 9t + -16t2 Solving 0 = 41 + 9t + -16t2 Solving for variable 't'. Combine like terms: 0 + -41 = -41 -41 + -9t + 16t2 = 41 + 9t + -16t2 + -41 + -9t + 16t2 Reorder the terms: -41 + -9t + 16t2 = 41 + -41 + 9t + -9t + -16t2 + 16t2 Combine like terms: 41 + -41 = 0 -41 + -9t + 16t2 = 0 + 9t + -9t + -16t2 + 16t2 -41 + -9t + 16t2 = 9t + -9t + -16t2 + 16t2 Combine like terms: 9t + -9t = 0 -41 + -9t + 16t2 = 0 + -16t2 + 16t2 -41 + -9t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -41 + -9t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.5625 + -0.5625t + t2 = 0 Move the constant term to the right: Add '2.5625' to each side of the equation. -2.5625 + -0.5625t + 2.5625 + t2 = 0 + 2.5625 Reorder the terms: -2.5625 + 2.5625 + -0.5625t + t2 = 0 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + -0.5625t + t2 = 0 + 2.5625 -0.5625t + t2 = 0 + 2.5625 Combine like terms: 0 + 2.5625 = 2.5625 -0.5625t + t2 = 2.5625 The t term is -0.5625t. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625t + 0.0791015625 + t2 = 2.5625 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625t + t2 = 2.5625 + 0.0791015625 Combine like terms: 2.5625 + 0.0791015625 = 2.6416015625 0.0791015625 + -0.5625t + t2 = 2.6416015625 Factor a perfect square on the left side: (t + -0.28125)(t + -0.28125) = 2.6416015625 Calculate the square root of the right side: 1.625300453 Break this problem into two subproblems by setting (t + -0.28125) equal to 1.625300453 and -1.625300453.Subproblem 1
t + -0.28125 = 1.625300453 Simplifying t + -0.28125 = 1.625300453 Reorder the terms: -0.28125 + t = 1.625300453 Solving -0.28125 + t = 1.625300453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + t = 1.625300453 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + t = 1.625300453 + 0.28125 t = 1.625300453 + 0.28125 Combine like terms: 1.625300453 + 0.28125 = 1.906550453 t = 1.906550453 Simplifying t = 1.906550453Subproblem 2
t + -0.28125 = -1.625300453 Simplifying t + -0.28125 = -1.625300453 Reorder the terms: -0.28125 + t = -1.625300453 Solving -0.28125 + t = -1.625300453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + t = -1.625300453 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + t = -1.625300453 + 0.28125 t = -1.625300453 + 0.28125 Combine like terms: -1.625300453 + 0.28125 = -1.344050453 t = -1.344050453 Simplifying t = -1.344050453Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.906550453, -1.344050453}
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