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Simplifying 0 = 0.16t2 + 35t + 0.25 Reorder the terms: 0 = 0.25 + 35t + 0.16t2 Solving 0 = 0.25 + 35t + 0.16t2 Solving for variable 't'. Combine like terms: 0 + -0.25 = -0.25 -0.25 + -35t + -0.16t2 = 0.25 + 35t + 0.16t2 + -0.25 + -35t + -0.16t2 Reorder the terms: -0.25 + -35t + -0.16t2 = 0.25 + -0.25 + 35t + -35t + 0.16t2 + -0.16t2 Combine like terms: 0.25 + -0.25 = 0.00 -0.25 + -35t + -0.16t2 = 0.00 + 35t + -35t + 0.16t2 + -0.16t2 -0.25 + -35t + -0.16t2 = 35t + -35t + 0.16t2 + -0.16t2 Combine like terms: 35t + -35t = 0 -0.25 + -35t + -0.16t2 = 0 + 0.16t2 + -0.16t2 -0.25 + -35t + -0.16t2 = 0.16t2 + -0.16t2 Combine like terms: 0.16t2 + -0.16t2 = 0.00 -0.25 + -35t + -0.16t2 = 0.00 Begin completing the square. Divide all terms by -0.16 the coefficient of the squared term: Divide each side by '-0.16'. 1.5625 + 218.75t + t2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + 218.75t + -1.5625 + t2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + 218.75t + t2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + 218.75t + t2 = 0 + -1.5625 218.75t + t2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 218.75t + t2 = -1.5625 The t term is 218.75t. Take half its coefficient (109.375). Square it (11962.89063) and add it to both sides. Add '11962.89063' to each side of the equation. 218.75t + 11962.89063 + t2 = -1.5625 + 11962.89063 Reorder the terms: 11962.89063 + 218.75t + t2 = -1.5625 + 11962.89063 Combine like terms: -1.5625 + 11962.89063 = 11961.32813 11962.89063 + 218.75t + t2 = 11961.32813 Factor a perfect square on the left side: (t + 109.375)(t + 109.375) = 11961.32813 Calculate the square root of the right side: 109.367856932 Break this problem into two subproblems by setting (t + 109.375) equal to 109.367856932 and -109.367856932.Subproblem 1
t + 109.375 = 109.367856932 Simplifying t + 109.375 = 109.367856932 Reorder the terms: 109.375 + t = 109.367856932 Solving 109.375 + t = 109.367856932 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-109.375' to each side of the equation. 109.375 + -109.375 + t = 109.367856932 + -109.375 Combine like terms: 109.375 + -109.375 = 0.000 0.000 + t = 109.367856932 + -109.375 t = 109.367856932 + -109.375 Combine like terms: 109.367856932 + -109.375 = -0.007143068 t = -0.007143068 Simplifying t = -0.007143068Subproblem 2
t + 109.375 = -109.367856932 Simplifying t + 109.375 = -109.367856932 Reorder the terms: 109.375 + t = -109.367856932 Solving 109.375 + t = -109.367856932 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-109.375' to each side of the equation. 109.375 + -109.375 + t = -109.367856932 + -109.375 Combine like terms: 109.375 + -109.375 = 0.000 0.000 + t = -109.367856932 + -109.375 t = -109.367856932 + -109.375 Combine like terms: -109.367856932 + -109.375 = -218.742856932 t = -218.742856932 Simplifying t = -218.742856932Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.007143068, -218.742856932}
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