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Simplifying 0.05t2 + 5t = 7000 Reorder the terms: 5t + 0.05t2 = 7000 Solving 5t + 0.05t2 = 7000 Solving for variable 't'. Reorder the terms: -7000 + 5t + 0.05t2 = 7000 + -7000 Combine like terms: 7000 + -7000 = 0 -7000 + 5t + 0.05t2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -140000 + 100t + t2 = 0 Move the constant term to the right: Add '140000' to each side of the equation. -140000 + 100t + 140000 + t2 = 0 + 140000 Reorder the terms: -140000 + 140000 + 100t + t2 = 0 + 140000 Combine like terms: -140000 + 140000 = 0 0 + 100t + t2 = 0 + 140000 100t + t2 = 0 + 140000 Combine like terms: 0 + 140000 = 140000 100t + t2 = 140000 The t term is 100t. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100t + 2500 + t2 = 140000 + 2500 Reorder the terms: 2500 + 100t + t2 = 140000 + 2500 Combine like terms: 140000 + 2500 = 142500 2500 + 100t + t2 = 142500 Factor a perfect square on the left side: (t + 50)(t + 50) = 142500 Calculate the square root of the right side: 377.491721764 Break this problem into two subproblems by setting (t + 50) equal to 377.491721764 and -377.491721764.Subproblem 1
t + 50 = 377.491721764 Simplifying t + 50 = 377.491721764 Reorder the terms: 50 + t = 377.491721764 Solving 50 + t = 377.491721764 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + t = 377.491721764 + -50 Combine like terms: 50 + -50 = 0 0 + t = 377.491721764 + -50 t = 377.491721764 + -50 Combine like terms: 377.491721764 + -50 = 327.491721764 t = 327.491721764 Simplifying t = 327.491721764Subproblem 2
t + 50 = -377.491721764 Simplifying t + 50 = -377.491721764 Reorder the terms: 50 + t = -377.491721764 Solving 50 + t = -377.491721764 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + t = -377.491721764 + -50 Combine like terms: 50 + -50 = 0 0 + t = -377.491721764 + -50 t = -377.491721764 + -50 Combine like terms: -377.491721764 + -50 = -427.491721764 t = -427.491721764 Simplifying t = -427.491721764Solution
The solution to the problem is based on the solutions from the subproblems. t = {327.491721764, -427.491721764}
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