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Simplifying 0 = 294t + -4.9t2 + -2450 Reorder the terms: 0 = -2450 + 294t + -4.9t2 Solving 0 = -2450 + 294t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + 2450 = 2450 2450 + -294t + 4.9t2 = -2450 + 294t + -4.9t2 + 2450 + -294t + 4.9t2 Reorder the terms: 2450 + -294t + 4.9t2 = -2450 + 2450 + 294t + -294t + -4.9t2 + 4.9t2 Combine like terms: -2450 + 2450 = 0 2450 + -294t + 4.9t2 = 0 + 294t + -294t + -4.9t2 + 4.9t2 2450 + -294t + 4.9t2 = 294t + -294t + -4.9t2 + 4.9t2 Combine like terms: 294t + -294t = 0 2450 + -294t + 4.9t2 = 0 + -4.9t2 + 4.9t2 2450 + -294t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 2450 + -294t + 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'. 500 + -60t + t2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -60t + -500 + t2 = 0 + -500 Reorder the terms: 500 + -500 + -60t + t2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -60t + t2 = 0 + -500 -60t + t2 = 0 + -500 Combine like terms: 0 + -500 = -500 -60t + t2 = -500 The t term is -60t. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60t + 900 + t2 = -500 + 900 Reorder the terms: 900 + -60t + t2 = -500 + 900 Combine like terms: -500 + 900 = 400 900 + -60t + t2 = 400 Factor a perfect square on the left side: (t + -30)(t + -30) = 400 Calculate the square root of the right side: 20 Break this problem into two subproblems by setting (t + -30) equal to 20 and -20.Subproblem 1
t + -30 = 20 Simplifying t + -30 = 20 Reorder the terms: -30 + t = 20 Solving -30 + t = 20 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = 20 + 30 Combine like terms: -30 + 30 = 0 0 + t = 20 + 30 t = 20 + 30 Combine like terms: 20 + 30 = 50 t = 50 Simplifying t = 50Subproblem 2
t + -30 = -20 Simplifying t + -30 = -20 Reorder the terms: -30 + t = -20 Solving -30 + t = -20 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = -20 + 30 Combine like terms: -30 + 30 = 0 0 + t = -20 + 30 t = -20 + 30 Combine like terms: -20 + 30 = 10 t = 10 Simplifying t = 10Solution
The solution to the problem is based on the solutions from the subproblems. t = {50, 10}
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