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Simplifying -0.0462t2 + -0.2592t + 1.861 = 0 Reorder the terms: 1.861 + -0.2592t + -0.0462t2 = 0 Solving 1.861 + -0.2592t + -0.0462t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.0462 the coefficient of the squared term: Divide each side by '-0.0462'. -40.28138528 + 5.61038961t + t2 = 0 Move the constant term to the right: Add '40.28138528' to each side of the equation. -40.28138528 + 5.61038961t + 40.28138528 + t2 = 0 + 40.28138528 Reorder the terms: -40.28138528 + 40.28138528 + 5.61038961t + t2 = 0 + 40.28138528 Combine like terms: -40.28138528 + 40.28138528 = 0.00000000 0.00000000 + 5.61038961t + t2 = 0 + 40.28138528 5.61038961t + t2 = 0 + 40.28138528 Combine like terms: 0 + 40.28138528 = 40.28138528 5.61038961t + t2 = 40.28138528 The t term is 5.61038961t. Take half its coefficient (2.805194805). Square it (7.869117894) and add it to both sides. Add '7.869117894' to each side of the equation. 5.61038961t + 7.869117894 + t2 = 40.28138528 + 7.869117894 Reorder the terms: 7.869117894 + 5.61038961t + t2 = 40.28138528 + 7.869117894 Combine like terms: 40.28138528 + 7.869117894 = 48.150503174 7.869117894 + 5.61038961t + t2 = 48.150503174 Factor a perfect square on the left side: (t + 2.805194805)(t + 2.805194805) = 48.150503174 Calculate the square root of the right side: 6.93905636 Break this problem into two subproblems by setting (t + 2.805194805) equal to 6.93905636 and -6.93905636.Subproblem 1
t + 2.805194805 = 6.93905636 Simplifying t + 2.805194805 = 6.93905636 Reorder the terms: 2.805194805 + t = 6.93905636 Solving 2.805194805 + t = 6.93905636 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.805194805' to each side of the equation. 2.805194805 + -2.805194805 + t = 6.93905636 + -2.805194805 Combine like terms: 2.805194805 + -2.805194805 = 0.000000000 0.000000000 + t = 6.93905636 + -2.805194805 t = 6.93905636 + -2.805194805 Combine like terms: 6.93905636 + -2.805194805 = 4.133861555 t = 4.133861555 Simplifying t = 4.133861555Subproblem 2
t + 2.805194805 = -6.93905636 Simplifying t + 2.805194805 = -6.93905636 Reorder the terms: 2.805194805 + t = -6.93905636 Solving 2.805194805 + t = -6.93905636 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.805194805' to each side of the equation. 2.805194805 + -2.805194805 + t = -6.93905636 + -2.805194805 Combine like terms: 2.805194805 + -2.805194805 = 0.000000000 0.000000000 + t = -6.93905636 + -2.805194805 t = -6.93905636 + -2.805194805 Combine like terms: -6.93905636 + -2.805194805 = -9.744251165 t = -9.744251165 Simplifying t = -9.744251165Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.133861555, -9.744251165}
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