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Simplifying 0.05t2 + -3t + -90 = 0 Reorder the terms: -90 + -3t + 0.05t2 = 0 Solving -90 + -3t + 0.05t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -1800 + -60t + t2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + -60t + 1800 + t2 = 0 + 1800 Reorder the terms: -1800 + 1800 + -60t + t2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + -60t + t2 = 0 + 1800 -60t + t2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 -60t + t2 = 1800 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 = 1800 + 900 Reorder the terms: 900 + -60t + t2 = 1800 + 900 Combine like terms: 1800 + 900 = 2700 900 + -60t + t2 = 2700 Factor a perfect square on the left side: (t + -30)(t + -30) = 2700 Calculate the square root of the right side: 51.961524227 Break this problem into two subproblems by setting (t + -30) equal to 51.961524227 and -51.961524227.Subproblem 1
t + -30 = 51.961524227 Simplifying t + -30 = 51.961524227 Reorder the terms: -30 + t = 51.961524227 Solving -30 + t = 51.961524227 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 = 51.961524227 + 30 Combine like terms: -30 + 30 = 0 0 + t = 51.961524227 + 30 t = 51.961524227 + 30 Combine like terms: 51.961524227 + 30 = 81.961524227 t = 81.961524227 Simplifying t = 81.961524227Subproblem 2
t + -30 = -51.961524227 Simplifying t + -30 = -51.961524227 Reorder the terms: -30 + t = -51.961524227 Solving -30 + t = -51.961524227 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 = -51.961524227 + 30 Combine like terms: -30 + 30 = 0 0 + t = -51.961524227 + 30 t = -51.961524227 + 30 Combine like terms: -51.961524227 + 30 = -21.961524227 t = -21.961524227 Simplifying t = -21.961524227Solution
The solution to the problem is based on the solutions from the subproblems. t = {81.961524227, -21.961524227}
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