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Simplifying 4 = -16t2 + 20t + 13 Reorder the terms: 4 = 13 + 20t + -16t2 Solving 4 = 13 + 20t + -16t2 Solving for variable 't'. Combine like terms: 4 + -13 = -9 -9 + -20t + 16t2 = 13 + 20t + -16t2 + -13 + -20t + 16t2 Reorder the terms: -9 + -20t + 16t2 = 13 + -13 + 20t + -20t + -16t2 + 16t2 Combine like terms: 13 + -13 = 0 -9 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2 -9 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 -9 + -20t + 16t2 = 0 + -16t2 + 16t2 -9 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -9 + -20t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + -1.25t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -1.25t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -1.25t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -1.25t + t2 = 0 + 0.5625 -1.25t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -1.25t + t2 = 0.5625 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = 0.5625 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 0.5625 + 0.390625 Combine like terms: 0.5625 + 0.390625 = 0.953125 0.390625 + -1.25t + t2 = 0.953125 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 0.953125 Calculate the square root of the right side: 0.976281209 Break this problem into two subproblems by setting (t + -0.625) equal to 0.976281209 and -0.976281209.Subproblem 1
t + -0.625 = 0.976281209 Simplifying t + -0.625 = 0.976281209 Reorder the terms: -0.625 + t = 0.976281209 Solving -0.625 + t = 0.976281209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 0.976281209 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 0.976281209 + 0.625 t = 0.976281209 + 0.625 Combine like terms: 0.976281209 + 0.625 = 1.601281209 t = 1.601281209 Simplifying t = 1.601281209Subproblem 2
t + -0.625 = -0.976281209 Simplifying t + -0.625 = -0.976281209 Reorder the terms: -0.625 + t = -0.976281209 Solving -0.625 + t = -0.976281209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -0.976281209 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -0.976281209 + 0.625 t = -0.976281209 + 0.625 Combine like terms: -0.976281209 + 0.625 = -0.351281209 t = -0.351281209 Simplifying t = -0.351281209Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.601281209, -0.351281209}
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