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Simplifying -16t2 + 13t + 22 = 0 Reorder the terms: 22 + 13t + -16t2 = 0 Solving 22 + 13t + -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'. -1.375 + -0.8125t + t2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -0.8125t + 1.375 + t2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -0.8125t + t2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -0.8125t + t2 = 0 + 1.375 -0.8125t + t2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -0.8125t + t2 = 1.375 The t term is -0.8125t. Take half its coefficient (-0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. -0.8125t + 0.1650390625 + t2 = 1.375 + 0.1650390625 Reorder the terms: 0.1650390625 + -0.8125t + t2 = 1.375 + 0.1650390625 Combine like terms: 1.375 + 0.1650390625 = 1.5400390625 0.1650390625 + -0.8125t + t2 = 1.5400390625 Factor a perfect square on the left side: (t + -0.40625)(t + -0.40625) = 1.5400390625 Calculate the square root of the right side: 1.240983103 Break this problem into two subproblems by setting (t + -0.40625) equal to 1.240983103 and -1.240983103.Subproblem 1
t + -0.40625 = 1.240983103 Simplifying t + -0.40625 = 1.240983103 Reorder the terms: -0.40625 + t = 1.240983103 Solving -0.40625 + t = 1.240983103 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + t = 1.240983103 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = 1.240983103 + 0.40625 t = 1.240983103 + 0.40625 Combine like terms: 1.240983103 + 0.40625 = 1.647233103 t = 1.647233103 Simplifying t = 1.647233103Subproblem 2
t + -0.40625 = -1.240983103 Simplifying t + -0.40625 = -1.240983103 Reorder the terms: -0.40625 + t = -1.240983103 Solving -0.40625 + t = -1.240983103 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + t = -1.240983103 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = -1.240983103 + 0.40625 t = -1.240983103 + 0.40625 Combine like terms: -1.240983103 + 0.40625 = -0.834733103 t = -0.834733103 Simplifying t = -0.834733103Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.647233103, -0.834733103}
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