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Simplifying 0 = -4.9t2 + 2500t + 1 Reorder the terms: 0 = 1 + 2500t + -4.9t2 Solving 0 = 1 + 2500t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -2500t + 4.9t2 = 1 + 2500t + -4.9t2 + -1 + -2500t + 4.9t2 Reorder the terms: -1 + -2500t + 4.9t2 = 1 + -1 + 2500t + -2500t + -4.9t2 + 4.9t2 Combine like terms: 1 + -1 = 0 -1 + -2500t + 4.9t2 = 0 + 2500t + -2500t + -4.9t2 + 4.9t2 -1 + -2500t + 4.9t2 = 2500t + -2500t + -4.9t2 + 4.9t2 Combine like terms: 2500t + -2500t = 0 -1 + -2500t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -1 + -2500t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1 + -2500t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.2040816327 + -510.2040816t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -510.2040816t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -510.2040816t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -510.2040816t + t2 = 0 + 0.2040816327 -510.2040816t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -510.2040816t + t2 = 0.2040816327 The t term is -510.2040816t. Take half its coefficient (-255.1020408). Square it (65077.05122) and add it to both sides. Add '65077.05122' to each side of the equation. -510.2040816t + 65077.05122 + t2 = 0.2040816327 + 65077.05122 Reorder the terms: 65077.05122 + -510.2040816t + t2 = 0.2040816327 + 65077.05122 Combine like terms: 0.2040816327 + 65077.05122 = 65077.2553016327 65077.05122 + -510.2040816t + t2 = 65077.2553016327 Factor a perfect square on the left side: (t + -255.1020408)(t + -255.1020408) = 65077.2553016327 Calculate the square root of the right side: 255.102440799 Break this problem into two subproblems by setting (t + -255.1020408) equal to 255.102440799 and -255.102440799.Subproblem 1
t + -255.1020408 = 255.102440799 Simplifying t + -255.1020408 = 255.102440799 Reorder the terms: -255.1020408 + t = 255.102440799 Solving -255.1020408 + t = 255.102440799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '255.1020408' to each side of the equation. -255.1020408 + 255.1020408 + t = 255.102440799 + 255.1020408 Combine like terms: -255.1020408 + 255.1020408 = 0.0000000 0.0000000 + t = 255.102440799 + 255.1020408 t = 255.102440799 + 255.1020408 Combine like terms: 255.102440799 + 255.1020408 = 510.204481599 t = 510.204481599 Simplifying t = 510.204481599Subproblem 2
t + -255.1020408 = -255.102440799 Simplifying t + -255.1020408 = -255.102440799 Reorder the terms: -255.1020408 + t = -255.102440799 Solving -255.1020408 + t = -255.102440799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '255.1020408' to each side of the equation. -255.1020408 + 255.1020408 + t = -255.102440799 + 255.1020408 Combine like terms: -255.1020408 + 255.1020408 = 0.0000000 0.0000000 + t = -255.102440799 + 255.1020408 t = -255.102440799 + 255.1020408 Combine like terms: -255.102440799 + 255.1020408 = -0.000399999 t = -0.000399999 Simplifying t = -0.000399999Solution
The solution to the problem is based on the solutions from the subproblems. t = {510.204481599, -0.000399999}
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