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Simplifying 0.0765t2 + -0.886t + 1.832 = 0 Reorder the terms: 1.832 + -0.886t + 0.0765t2 = 0 Solving 1.832 + -0.886t + 0.0765t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0765 the coefficient of the squared term: Divide each side by '0.0765'. 23.94771242 + -11.58169935t + t2 = 0 Move the constant term to the right: Add '-23.94771242' to each side of the equation. 23.94771242 + -11.58169935t + -23.94771242 + t2 = 0 + -23.94771242 Reorder the terms: 23.94771242 + -23.94771242 + -11.58169935t + t2 = 0 + -23.94771242 Combine like terms: 23.94771242 + -23.94771242 = 0.00000000 0.00000000 + -11.58169935t + t2 = 0 + -23.94771242 -11.58169935t + t2 = 0 + -23.94771242 Combine like terms: 0 + -23.94771242 = -23.94771242 -11.58169935t + t2 = -23.94771242 The t term is -11.58169935t. Take half its coefficient (-5.790849675). Square it (33.53393996) and add it to both sides. Add '33.53393996' to each side of the equation. -11.58169935t + 33.53393996 + t2 = -23.94771242 + 33.53393996 Reorder the terms: 33.53393996 + -11.58169935t + t2 = -23.94771242 + 33.53393996 Combine like terms: -23.94771242 + 33.53393996 = 9.58622754 33.53393996 + -11.58169935t + t2 = 9.58622754 Factor a perfect square on the left side: (t + -5.790849675)(t + -5.790849675) = 9.58622754 Calculate the square root of the right side: 3.096163358 Break this problem into two subproblems by setting (t + -5.790849675) equal to 3.096163358 and -3.096163358.Subproblem 1
t + -5.790849675 = 3.096163358 Simplifying t + -5.790849675 = 3.096163358 Reorder the terms: -5.790849675 + t = 3.096163358 Solving -5.790849675 + t = 3.096163358 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.790849675' to each side of the equation. -5.790849675 + 5.790849675 + t = 3.096163358 + 5.790849675 Combine like terms: -5.790849675 + 5.790849675 = 0.000000000 0.000000000 + t = 3.096163358 + 5.790849675 t = 3.096163358 + 5.790849675 Combine like terms: 3.096163358 + 5.790849675 = 8.887013033 t = 8.887013033 Simplifying t = 8.887013033Subproblem 2
t + -5.790849675 = -3.096163358 Simplifying t + -5.790849675 = -3.096163358 Reorder the terms: -5.790849675 + t = -3.096163358 Solving -5.790849675 + t = -3.096163358 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.790849675' to each side of the equation. -5.790849675 + 5.790849675 + t = -3.096163358 + 5.790849675 Combine like terms: -5.790849675 + 5.790849675 = 0.000000000 0.000000000 + t = -3.096163358 + 5.790849675 t = -3.096163358 + 5.790849675 Combine like terms: -3.096163358 + 5.790849675 = 2.694686317 t = 2.694686317 Simplifying t = 2.694686317Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.887013033, 2.694686317}
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