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Simplifying -93 = -16t2 + 63t Reorder the terms: -93 = 63t + -16t2 Solving -93 = 63t + -16t2 Solving for variable 't'. Reorder the terms: -93 + -63t + 16t2 = 63t + -63t + -16t2 + 16t2 Combine like terms: 63t + -63t = 0 -93 + -63t + 16t2 = 0 + -16t2 + 16t2 -93 + -63t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -93 + -63t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.8125 + -3.9375t + t2 = 0 Move the constant term to the right: Add '5.8125' to each side of the equation. -5.8125 + -3.9375t + 5.8125 + t2 = 0 + 5.8125 Reorder the terms: -5.8125 + 5.8125 + -3.9375t + t2 = 0 + 5.8125 Combine like terms: -5.8125 + 5.8125 = 0.0000 0.0000 + -3.9375t + t2 = 0 + 5.8125 -3.9375t + t2 = 0 + 5.8125 Combine like terms: 0 + 5.8125 = 5.8125 -3.9375t + t2 = 5.8125 The t term is -3.9375t. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375t + 3.875976563 + t2 = 5.8125 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375t + t2 = 5.8125 + 3.875976563 Combine like terms: 5.8125 + 3.875976563 = 9.688476563 3.875976563 + -3.9375t + t2 = 9.688476563 Factor a perfect square on the left side: (t + -1.96875)(t + -1.96875) = 9.688476563 Calculate the square root of the right side: 3.112631774 Break this problem into two subproblems by setting (t + -1.96875) equal to 3.112631774 and -3.112631774.Subproblem 1
t + -1.96875 = 3.112631774 Simplifying t + -1.96875 = 3.112631774 Reorder the terms: -1.96875 + t = 3.112631774 Solving -1.96875 + t = 3.112631774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + t = 3.112631774 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + t = 3.112631774 + 1.96875 t = 3.112631774 + 1.96875 Combine like terms: 3.112631774 + 1.96875 = 5.081381774 t = 5.081381774 Simplifying t = 5.081381774Subproblem 2
t + -1.96875 = -3.112631774 Simplifying t + -1.96875 = -3.112631774 Reorder the terms: -1.96875 + t = -3.112631774 Solving -1.96875 + t = -3.112631774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + t = -3.112631774 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + t = -3.112631774 + 1.96875 t = -3.112631774 + 1.96875 Combine like terms: -3.112631774 + 1.96875 = -1.143881774 t = -1.143881774 Simplifying t = -1.143881774Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.081381774, -1.143881774}
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