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Simplifying 16t2 + -141t + -112 = 0 Reorder the terms: -112 + -141t + 16t2 = 0 Solving -112 + -141t + 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'. -7 + -8.8125t + t2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -8.8125t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + -8.8125t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8.8125t + t2 = 0 + 7 -8.8125t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 -8.8125t + t2 = 7 The t term is -8.8125t. Take half its coefficient (-4.40625). Square it (19.41503906) and add it to both sides. Add '19.41503906' to each side of the equation. -8.8125t + 19.41503906 + t2 = 7 + 19.41503906 Reorder the terms: 19.41503906 + -8.8125t + t2 = 7 + 19.41503906 Combine like terms: 7 + 19.41503906 = 26.41503906 19.41503906 + -8.8125t + t2 = 26.41503906 Factor a perfect square on the left side: (t + -4.40625)(t + -4.40625) = 26.41503906 Calculate the square root of the right side: 5.13955631 Break this problem into two subproblems by setting (t + -4.40625) equal to 5.13955631 and -5.13955631.Subproblem 1
t + -4.40625 = 5.13955631 Simplifying t + -4.40625 = 5.13955631 Reorder the terms: -4.40625 + t = 5.13955631 Solving -4.40625 + t = 5.13955631 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.40625' to each side of the equation. -4.40625 + 4.40625 + t = 5.13955631 + 4.40625 Combine like terms: -4.40625 + 4.40625 = 0.00000 0.00000 + t = 5.13955631 + 4.40625 t = 5.13955631 + 4.40625 Combine like terms: 5.13955631 + 4.40625 = 9.54580631 t = 9.54580631 Simplifying t = 9.54580631Subproblem 2
t + -4.40625 = -5.13955631 Simplifying t + -4.40625 = -5.13955631 Reorder the terms: -4.40625 + t = -5.13955631 Solving -4.40625 + t = -5.13955631 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.40625' to each side of the equation. -4.40625 + 4.40625 + t = -5.13955631 + 4.40625 Combine like terms: -4.40625 + 4.40625 = 0.00000 0.00000 + t = -5.13955631 + 4.40625 t = -5.13955631 + 4.40625 Combine like terms: -5.13955631 + 4.40625 = -0.73330631 t = -0.73330631 Simplifying t = -0.73330631Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.54580631, -0.73330631}
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