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Simplifying 540 = 72t + 1.2t2 Solving 540 = 72t + 1.2t2 Solving for variable 't'. Reorder the terms: 540 + -72t + -1.2t2 = 72t + -72t + 1.2t2 + -1.2t2 Combine like terms: 72t + -72t = 0 540 + -72t + -1.2t2 = 0 + 1.2t2 + -1.2t2 540 + -72t + -1.2t2 = 1.2t2 + -1.2t2 Combine like terms: 1.2t2 + -1.2t2 = 0.0 540 + -72t + -1.2t2 = 0.0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. -450 + 60t + t2 = 0 Move the constant term to the right: Add '450' to each side of the equation. -450 + 60t + 450 + t2 = 0 + 450 Reorder the terms: -450 + 450 + 60t + t2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 60t + t2 = 0 + 450 60t + t2 = 0 + 450 Combine like terms: 0 + 450 = 450 60t + t2 = 450 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 = 450 + 900 Reorder the terms: 900 + 60t + t2 = 450 + 900 Combine like terms: 450 + 900 = 1350 900 + 60t + t2 = 1350 Factor a perfect square on the left side: (t + 30)(t + 30) = 1350 Calculate the square root of the right side: 36.742346142 Break this problem into two subproblems by setting (t + 30) equal to 36.742346142 and -36.742346142.Subproblem 1
t + 30 = 36.742346142 Simplifying t + 30 = 36.742346142 Reorder the terms: 30 + t = 36.742346142 Solving 30 + t = 36.742346142 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 = 36.742346142 + -30 Combine like terms: 30 + -30 = 0 0 + t = 36.742346142 + -30 t = 36.742346142 + -30 Combine like terms: 36.742346142 + -30 = 6.742346142 t = 6.742346142 Simplifying t = 6.742346142Subproblem 2
t + 30 = -36.742346142 Simplifying t + 30 = -36.742346142 Reorder the terms: 30 + t = -36.742346142 Solving 30 + t = -36.742346142 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 = -36.742346142 + -30 Combine like terms: 30 + -30 = 0 0 + t = -36.742346142 + -30 t = -36.742346142 + -30 Combine like terms: -36.742346142 + -30 = -66.742346142 t = -66.742346142 Simplifying t = -66.742346142Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.742346142, -66.742346142}
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