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Simplifying 432.25 = t2 + 60t Reorder the terms: 432.25 = 60t + t2 Solving 432.25 = 60t + t2 Solving for variable 't'. Reorder the terms: 432.25 + -60t + -1t2 = 60t + -60t + t2 + -1t2 Combine like terms: 60t + -60t = 0 432.25 + -60t + -1t2 = 0 + t2 + -1t2 432.25 + -60t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 432.25 + -60t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -432.25 + 60t + t2 = 0 Move the constant term to the right: Add '432.25' to each side of the equation. -432.25 + 60t + 432.25 + t2 = 0 + 432.25 Reorder the terms: -432.25 + 432.25 + 60t + t2 = 0 + 432.25 Combine like terms: -432.25 + 432.25 = 0.00 0.00 + 60t + t2 = 0 + 432.25 60t + t2 = 0 + 432.25 Combine like terms: 0 + 432.25 = 432.25 60t + t2 = 432.25 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 = 432.25 + 900 Reorder the terms: 900 + 60t + t2 = 432.25 + 900 Combine like terms: 432.25 + 900 = 1332.25 900 + 60t + t2 = 1332.25 Factor a perfect square on the left side: (t + 30)(t + 30) = 1332.25 Calculate the square root of the right side: 36.5 Break this problem into two subproblems by setting (t + 30) equal to 36.5 and -36.5.Subproblem 1
t + 30 = 36.5 Simplifying t + 30 = 36.5 Reorder the terms: 30 + t = 36.5 Solving 30 + t = 36.5 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 = 36.5 + -30 Combine like terms: 30 + -30 = 0 0 + t = 36.5 + -30 t = 36.5 + -30 Combine like terms: 36.5 + -30 = 6.5 t = 6.5 Simplifying t = 6.5Subproblem 2
t + 30 = -36.5 Simplifying t + 30 = -36.5 Reorder the terms: 30 + t = -36.5 Solving 30 + t = -36.5 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 = -36.5 + -30 Combine like terms: 30 + -30 = 0 0 + t = -36.5 + -30 t = -36.5 + -30 Combine like terms: -36.5 + -30 = -66.5 t = -66.5 Simplifying t = -66.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.5, -66.5}
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