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Simplifying 100 = (400t) + (0.5(-2) * t2) Multiply 0.5 * -2 100 = (400t) + (-1t2) Solving 100 = (400t) + (-1t2) Solving for variable 't'. 100 + (-400t) + t2 = (400t) + (-1t2) + (-400t) + (t2) 100 + (-400t) + t2 = (400t) + (-1t2) + (-400t) + t2 Reorder the terms: 100 + (-400t) + t2 = (400t) + (-400t) + (-1t2) + t2 Combine like terms: (400t) + (-400t) = 0 100 + (-400t) + t2 = 0 + (-1t2) + t2 100 + (-400t) + t2 = (-1t2) + t2 Combine like terms: (-1t2) + t2 = 0 100 + (-400t) + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + (-400t) + -100 + t2 = 0 + -100 Reorder the terms: 100 + -100 + (-400t) + t2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + (-400t) + t2 = 0 + -100 (-400t) + t2 = 0 + -100 Combine like terms: 0 + -100 = -100 (-400t) + t2 = -100 The t term is (-400t). Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. (-400t) + 40000 + t2 = -100 + 40000 Reorder the terms: 40000 + (-400t) + t2 = -100 + 40000 Combine like terms: -100 + 40000 = 39900 40000 + (-400t) + t2 = 39900 Factor a perfect square on the left side: (t + -200)(t + -200) = 39900 Calculate the square root of the right side: 199.749843554 Break this problem into two subproblems by setting (t + -200) equal to 199.749843554 and -199.749843554.Subproblem 1
t + -200 = 199.749843554 Simplifying t + -200 = 199.749843554 Reorder the terms: -200 + t = 199.749843554 Solving -200 + t = 199.749843554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + t = 199.749843554 + 200 Combine like terms: -200 + 200 = 0 0 + t = 199.749843554 + 200 t = 199.749843554 + 200 Combine like terms: 199.749843554 + 200 = 399.749843554 t = 399.749843554 Simplifying t = 399.749843554Subproblem 2
t + -200 = -199.749843554 Simplifying t + -200 = -199.749843554 Reorder the terms: -200 + t = -199.749843554 Solving -200 + t = -199.749843554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + t = -199.749843554 + 200 Combine like terms: -200 + 200 = 0 0 + t = -199.749843554 + 200 t = -199.749843554 + 200 Combine like terms: -199.749843554 + 200 = 0.250156446 t = 0.250156446 Simplifying t = 0.250156446Solution
The solution to the problem is based on the solutions from the subproblems. t = {399.749843554, 0.250156446}
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