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Simplifying 16t2 + 40t + 3 = 330 Reorder the terms: 3 + 40t + 16t2 = 330 Solving 3 + 40t + 16t2 = 330 Solving for variable 't'. Reorder the terms: 3 + -330 + 40t + 16t2 = 330 + -330 Combine like terms: 3 + -330 = -327 -327 + 40t + 16t2 = 330 + -330 Combine like terms: 330 + -330 = 0 -327 + 40t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -20.4375 + 2.5t + t2 = 0 Move the constant term to the right: Add '20.4375' to each side of the equation. -20.4375 + 2.5t + 20.4375 + t2 = 0 + 20.4375 Reorder the terms: -20.4375 + 20.4375 + 2.5t + t2 = 0 + 20.4375 Combine like terms: -20.4375 + 20.4375 = 0.0000 0.0000 + 2.5t + t2 = 0 + 20.4375 2.5t + t2 = 0 + 20.4375 Combine like terms: 0 + 20.4375 = 20.4375 2.5t + t2 = 20.4375 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 20.4375 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 20.4375 + 1.5625 Combine like terms: 20.4375 + 1.5625 = 22 1.5625 + 2.5t + t2 = 22 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (t + 1.25) equal to 4.69041576 and -4.69041576.Subproblem 1
t + 1.25 = 4.69041576 Simplifying t + 1.25 = 4.69041576 Reorder the terms: 1.25 + t = 4.69041576 Solving 1.25 + t = 4.69041576 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 4.69041576 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 4.69041576 + -1.25 t = 4.69041576 + -1.25 Combine like terms: 4.69041576 + -1.25 = 3.44041576 t = 3.44041576 Simplifying t = 3.44041576Subproblem 2
t + 1.25 = -4.69041576 Simplifying t + 1.25 = -4.69041576 Reorder the terms: 1.25 + t = -4.69041576 Solving 1.25 + t = -4.69041576 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -4.69041576 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -4.69041576 + -1.25 t = -4.69041576 + -1.25 Combine like terms: -4.69041576 + -1.25 = -5.94041576 t = -5.94041576 Simplifying t = -5.94041576Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.44041576, -5.94041576}
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