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Simplifying -2 = -16t2 + 31t + 6 Reorder the terms: -2 = 6 + 31t + -16t2 Solving -2 = 6 + 31t + -16t2 Solving for variable 't'. Combine like terms: -2 + -6 = -8 -8 + -31t + 16t2 = 6 + 31t + -16t2 + -6 + -31t + 16t2 Reorder the terms: -8 + -31t + 16t2 = 6 + -6 + 31t + -31t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -8 + -31t + 16t2 = 0 + 31t + -31t + -16t2 + 16t2 -8 + -31t + 16t2 = 31t + -31t + -16t2 + 16t2 Combine like terms: 31t + -31t = 0 -8 + -31t + 16t2 = 0 + -16t2 + 16t2 -8 + -31t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -8 + -31t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5 + -1.9375t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.9375t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.9375t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.9375t + t2 = 0 + 0.5 -1.9375t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.9375t + t2 = 0.5 The t term is -1.9375t. Take half its coefficient (-0.96875). Square it (0.9384765625) and add it to both sides. Add '0.9384765625' to each side of the equation. -1.9375t + 0.9384765625 + t2 = 0.5 + 0.9384765625 Reorder the terms: 0.9384765625 + -1.9375t + t2 = 0.5 + 0.9384765625 Combine like terms: 0.5 + 0.9384765625 = 1.4384765625 0.9384765625 + -1.9375t + t2 = 1.4384765625 Factor a perfect square on the left side: (t + -0.96875)(t + -0.96875) = 1.4384765625 Calculate the square root of the right side: 1.199365066 Break this problem into two subproblems by setting (t + -0.96875) equal to 1.199365066 and -1.199365066.Subproblem 1
t + -0.96875 = 1.199365066 Simplifying t + -0.96875 = 1.199365066 Reorder the terms: -0.96875 + t = 1.199365066 Solving -0.96875 + t = 1.199365066 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + t = 1.199365066 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + t = 1.199365066 + 0.96875 t = 1.199365066 + 0.96875 Combine like terms: 1.199365066 + 0.96875 = 2.168115066 t = 2.168115066 Simplifying t = 2.168115066Subproblem 2
t + -0.96875 = -1.199365066 Simplifying t + -0.96875 = -1.199365066 Reorder the terms: -0.96875 + t = -1.199365066 Solving -0.96875 + t = -1.199365066 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + t = -1.199365066 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + t = -1.199365066 + 0.96875 t = -1.199365066 + 0.96875 Combine like terms: -1.199365066 + 0.96875 = -0.230615066 t = -0.230615066 Simplifying t = -0.230615066Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.168115066, -0.230615066}
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