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Simplifying 16t2 + -45t + 20 = 0 Reorder the terms: 20 + -45t + 16t2 = 0 Solving 20 + -45t + 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'. 1.25 + -2.8125t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2.8125t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2.8125t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2.8125t + t2 = 0 + -1.25 -2.8125t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2.8125t + t2 = -1.25 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = -1.25 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = -1.25 + 1.977539063 Combine like terms: -1.25 + 1.977539063 = 0.727539063 1.977539063 + -2.8125t + t2 = 0.727539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 0.727539063 Calculate the square root of the right side: 0.852959004 Break this problem into two subproblems by setting (t + -1.40625) equal to 0.852959004 and -0.852959004.Subproblem 1
t + -1.40625 = 0.852959004 Simplifying t + -1.40625 = 0.852959004 Reorder the terms: -1.40625 + t = 0.852959004 Solving -1.40625 + t = 0.852959004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 0.852959004 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 0.852959004 + 1.40625 t = 0.852959004 + 1.40625 Combine like terms: 0.852959004 + 1.40625 = 2.259209004 t = 2.259209004 Simplifying t = 2.259209004Subproblem 2
t + -1.40625 = -0.852959004 Simplifying t + -1.40625 = -0.852959004 Reorder the terms: -1.40625 + t = -0.852959004 Solving -1.40625 + t = -0.852959004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -0.852959004 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -0.852959004 + 1.40625 t = -0.852959004 + 1.40625 Combine like terms: -0.852959004 + 1.40625 = 0.553290996 t = 0.553290996 Simplifying t = 0.553290996Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.259209004, 0.553290996}
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