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Simplifying -16t2 + 77t + 5 = 0 Reorder the terms: 5 + 77t + -16t2 = 0 Solving 5 + 77t + -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'. -0.3125 + -4.8125t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -4.8125t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -4.8125t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -4.8125t + t2 = 0 + 0.3125 -4.8125t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -4.8125t + t2 = 0.3125 The t term is -4.8125t. Take half its coefficient (-2.40625). Square it (5.790039063) and add it to both sides. Add '5.790039063' to each side of the equation. -4.8125t + 5.790039063 + t2 = 0.3125 + 5.790039063 Reorder the terms: 5.790039063 + -4.8125t + t2 = 0.3125 + 5.790039063 Combine like terms: 0.3125 + 5.790039063 = 6.102539063 5.790039063 + -4.8125t + t2 = 6.102539063 Factor a perfect square on the left side: (t + -2.40625)(t + -2.40625) = 6.102539063 Calculate the square root of the right side: 2.470331772 Break this problem into two subproblems by setting (t + -2.40625) equal to 2.470331772 and -2.470331772.Subproblem 1
t + -2.40625 = 2.470331772 Simplifying t + -2.40625 = 2.470331772 Reorder the terms: -2.40625 + t = 2.470331772 Solving -2.40625 + t = 2.470331772 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.40625' to each side of the equation. -2.40625 + 2.40625 + t = 2.470331772 + 2.40625 Combine like terms: -2.40625 + 2.40625 = 0.00000 0.00000 + t = 2.470331772 + 2.40625 t = 2.470331772 + 2.40625 Combine like terms: 2.470331772 + 2.40625 = 4.876581772 t = 4.876581772 Simplifying t = 4.876581772Subproblem 2
t + -2.40625 = -2.470331772 Simplifying t + -2.40625 = -2.470331772 Reorder the terms: -2.40625 + t = -2.470331772 Solving -2.40625 + t = -2.470331772 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.40625' to each side of the equation. -2.40625 + 2.40625 + t = -2.470331772 + 2.40625 Combine like terms: -2.40625 + 2.40625 = 0.00000 0.00000 + t = -2.470331772 + 2.40625 t = -2.470331772 + 2.40625 Combine like terms: -2.470331772 + 2.40625 = -0.064081772 t = -0.064081772 Simplifying t = -0.064081772Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.876581772, -0.064081772}
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