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Simplifying -16t2 + 88t + 3 = 0 Reorder the terms: 3 + 88t + -16t2 = 0 Solving 3 + 88t + -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'. -0.1875 + -5.5t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -5.5t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -5.5t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -5.5t + t2 = 0 + 0.1875 -5.5t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -5.5t + t2 = 0.1875 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = 0.1875 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 0.1875 + 7.5625 Combine like terms: 0.1875 + 7.5625 = 7.75 7.5625 + -5.5t + t2 = 7.75 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (t + -2.75) equal to 2.783882181 and -2.783882181.Subproblem 1
t + -2.75 = 2.783882181 Simplifying t + -2.75 = 2.783882181 Reorder the terms: -2.75 + t = 2.783882181 Solving -2.75 + t = 2.783882181 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = 2.783882181 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.783882181 + 2.75 t = 2.783882181 + 2.75 Combine like terms: 2.783882181 + 2.75 = 5.533882181 t = 5.533882181 Simplifying t = 5.533882181Subproblem 2
t + -2.75 = -2.783882181 Simplifying t + -2.75 = -2.783882181 Reorder the terms: -2.75 + t = -2.783882181 Solving -2.75 + t = -2.783882181 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = -2.783882181 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.783882181 + 2.75 t = -2.783882181 + 2.75 Combine like terms: -2.783882181 + 2.75 = -0.033882181 t = -0.033882181 Simplifying t = -0.033882181Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.533882181, -0.033882181}
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