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Simplifying 0.85t2 + 6t + -1800 = 0 Reorder the terms: -1800 + 6t + 0.85t2 = 0 Solving -1800 + 6t + 0.85t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.85 the coefficient of the squared term: Divide each side by '0.85'. -2117.647059 + 7.058823529t + t2 = 0 Move the constant term to the right: Add '2117.647059' to each side of the equation. -2117.647059 + 7.058823529t + 2117.647059 + t2 = 0 + 2117.647059 Reorder the terms: -2117.647059 + 2117.647059 + 7.058823529t + t2 = 0 + 2117.647059 Combine like terms: -2117.647059 + 2117.647059 = 0.000000 0.000000 + 7.058823529t + t2 = 0 + 2117.647059 7.058823529t + t2 = 0 + 2117.647059 Combine like terms: 0 + 2117.647059 = 2117.647059 7.058823529t + t2 = 2117.647059 The t term is 7.058823529t. Take half its coefficient (3.529411765). Square it (12.45674741) and add it to both sides. Add '12.45674741' to each side of the equation. 7.058823529t + 12.45674741 + t2 = 2117.647059 + 12.45674741 Reorder the terms: 12.45674741 + 7.058823529t + t2 = 2117.647059 + 12.45674741 Combine like terms: 2117.647059 + 12.45674741 = 2130.10380641 12.45674741 + 7.058823529t + t2 = 2130.10380641 Factor a perfect square on the left side: (t + 3.529411765)(t + 3.529411765) = 2130.10380641 Calculate the square root of the right side: 46.153047639 Break this problem into two subproblems by setting (t + 3.529411765) equal to 46.153047639 and -46.153047639.Subproblem 1
t + 3.529411765 = 46.153047639 Simplifying t + 3.529411765 = 46.153047639 Reorder the terms: 3.529411765 + t = 46.153047639 Solving 3.529411765 + t = 46.153047639 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.529411765' to each side of the equation. 3.529411765 + -3.529411765 + t = 46.153047639 + -3.529411765 Combine like terms: 3.529411765 + -3.529411765 = 0.000000000 0.000000000 + t = 46.153047639 + -3.529411765 t = 46.153047639 + -3.529411765 Combine like terms: 46.153047639 + -3.529411765 = 42.623635874 t = 42.623635874 Simplifying t = 42.623635874Subproblem 2
t + 3.529411765 = -46.153047639 Simplifying t + 3.529411765 = -46.153047639 Reorder the terms: 3.529411765 + t = -46.153047639 Solving 3.529411765 + t = -46.153047639 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.529411765' to each side of the equation. 3.529411765 + -3.529411765 + t = -46.153047639 + -3.529411765 Combine like terms: 3.529411765 + -3.529411765 = 0.000000000 0.000000000 + t = -46.153047639 + -3.529411765 t = -46.153047639 + -3.529411765 Combine like terms: -46.153047639 + -3.529411765 = -49.682459404 t = -49.682459404 Simplifying t = -49.682459404Solution
The solution to the problem is based on the solutions from the subproblems. t = {42.623635874, -49.682459404}
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