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Simplifying 5t2 + 2t + -3600 = 0 Reorder the terms: -3600 + 2t + 5t2 = 0 Solving -3600 + 2t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -720 + 0.4t + t2 = 0 Move the constant term to the right: Add '720' to each side of the equation. -720 + 0.4t + 720 + t2 = 0 + 720 Reorder the terms: -720 + 720 + 0.4t + t2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + 0.4t + t2 = 0 + 720 0.4t + t2 = 0 + 720 Combine like terms: 0 + 720 = 720 0.4t + t2 = 720 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 720 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 720 + 0.04 Combine like terms: 720 + 0.04 = 720.04 0.04 + 0.4t + t2 = 720.04 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 720.04 Calculate the square root of the right side: 26.833561076 Break this problem into two subproblems by setting (t + 0.2) equal to 26.833561076 and -26.833561076.Subproblem 1
t + 0.2 = 26.833561076 Simplifying t + 0.2 = 26.833561076 Reorder the terms: 0.2 + t = 26.833561076 Solving 0.2 + t = 26.833561076 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 26.833561076 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 26.833561076 + -0.2 t = 26.833561076 + -0.2 Combine like terms: 26.833561076 + -0.2 = 26.633561076 t = 26.633561076 Simplifying t = 26.633561076Subproblem 2
t + 0.2 = -26.833561076 Simplifying t + 0.2 = -26.833561076 Reorder the terms: 0.2 + t = -26.833561076 Solving 0.2 + t = -26.833561076 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -26.833561076 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -26.833561076 + -0.2 t = -26.833561076 + -0.2 Combine like terms: -26.833561076 + -0.2 = -27.033561076 t = -27.033561076 Simplifying t = -27.033561076Solution
The solution to the problem is based on the solutions from the subproblems. t = {26.633561076, -27.033561076}
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