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Simplifying 0 = -16t2 + 47t + 6 Reorder the terms: 0 = 6 + 47t + -16t2 Solving 0 = 6 + 47t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -47t + 16t2 = 6 + 47t + -16t2 + -6 + -47t + 16t2 Reorder the terms: -6 + -47t + 16t2 = 6 + -6 + 47t + -47t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -47t + 16t2 = 0 + 47t + -47t + -16t2 + 16t2 -6 + -47t + 16t2 = 47t + -47t + -16t2 + 16t2 Combine like terms: 47t + -47t = 0 -6 + -47t + 16t2 = 0 + -16t2 + 16t2 -6 + -47t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -47t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + -2.9375t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -2.9375t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -2.9375t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -2.9375t + t2 = 0 + 0.375 -2.9375t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -2.9375t + t2 = 0.375 The t term is -2.9375t. Take half its coefficient (-1.46875). Square it (2.157226563) and add it to both sides. Add '2.157226563' to each side of the equation. -2.9375t + 2.157226563 + t2 = 0.375 + 2.157226563 Reorder the terms: 2.157226563 + -2.9375t + t2 = 0.375 + 2.157226563 Combine like terms: 0.375 + 2.157226563 = 2.532226563 2.157226563 + -2.9375t + t2 = 2.532226563 Factor a perfect square on the left side: (t + -1.46875)(t + -1.46875) = 2.532226563 Calculate the square root of the right side: 1.591297132 Break this problem into two subproblems by setting (t + -1.46875) equal to 1.591297132 and -1.591297132.Subproblem 1
t + -1.46875 = 1.591297132 Simplifying t + -1.46875 = 1.591297132 Reorder the terms: -1.46875 + t = 1.591297132 Solving -1.46875 + t = 1.591297132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.46875' to each side of the equation. -1.46875 + 1.46875 + t = 1.591297132 + 1.46875 Combine like terms: -1.46875 + 1.46875 = 0.00000 0.00000 + t = 1.591297132 + 1.46875 t = 1.591297132 + 1.46875 Combine like terms: 1.591297132 + 1.46875 = 3.060047132 t = 3.060047132 Simplifying t = 3.060047132Subproblem 2
t + -1.46875 = -1.591297132 Simplifying t + -1.46875 = -1.591297132 Reorder the terms: -1.46875 + t = -1.591297132 Solving -1.46875 + t = -1.591297132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.46875' to each side of the equation. -1.46875 + 1.46875 + t = -1.591297132 + 1.46875 Combine like terms: -1.46875 + 1.46875 = 0.00000 0.00000 + t = -1.591297132 + 1.46875 t = -1.591297132 + 1.46875 Combine like terms: -1.591297132 + 1.46875 = -0.122547132 t = -0.122547132 Simplifying t = -0.122547132Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.060047132, -0.122547132}
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