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Simplifying 9t2 + -2260t + 129600 = 0 Reorder the terms: 129600 + -2260t + 9t2 = 0 Solving 129600 + -2260t + 9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 14400 + -251.1111111t + t2 = 0 Move the constant term to the right: Add '-14400' to each side of the equation. 14400 + -251.1111111t + -14400 + t2 = 0 + -14400 Reorder the terms: 14400 + -14400 + -251.1111111t + t2 = 0 + -14400 Combine like terms: 14400 + -14400 = 0 0 + -251.1111111t + t2 = 0 + -14400 -251.1111111t + t2 = 0 + -14400 Combine like terms: 0 + -14400 = -14400 -251.1111111t + t2 = -14400 The t term is -251.1111111t. Take half its coefficient (-125.5555556). Square it (15764.19754) and add it to both sides. Add '15764.19754' to each side of the equation. -251.1111111t + 15764.19754 + t2 = -14400 + 15764.19754 Reorder the terms: 15764.19754 + -251.1111111t + t2 = -14400 + 15764.19754 Combine like terms: -14400 + 15764.19754 = 1364.19754 15764.19754 + -251.1111111t + t2 = 1364.19754 Factor a perfect square on the left side: (t + -125.5555556)(t + -125.5555556) = 1364.19754 Calculate the square root of the right side: 36.935044876 Break this problem into two subproblems by setting (t + -125.5555556) equal to 36.935044876 and -36.935044876.Subproblem 1
t + -125.5555556 = 36.935044876 Simplifying t + -125.5555556 = 36.935044876 Reorder the terms: -125.5555556 + t = 36.935044876 Solving -125.5555556 + t = 36.935044876 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '125.5555556' to each side of the equation. -125.5555556 + 125.5555556 + t = 36.935044876 + 125.5555556 Combine like terms: -125.5555556 + 125.5555556 = 0.0000000 0.0000000 + t = 36.935044876 + 125.5555556 t = 36.935044876 + 125.5555556 Combine like terms: 36.935044876 + 125.5555556 = 162.490600476 t = 162.490600476 Simplifying t = 162.490600476Subproblem 2
t + -125.5555556 = -36.935044876 Simplifying t + -125.5555556 = -36.935044876 Reorder the terms: -125.5555556 + t = -36.935044876 Solving -125.5555556 + t = -36.935044876 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '125.5555556' to each side of the equation. -125.5555556 + 125.5555556 + t = -36.935044876 + 125.5555556 Combine like terms: -125.5555556 + 125.5555556 = 0.0000000 0.0000000 + t = -36.935044876 + 125.5555556 t = -36.935044876 + 125.5555556 Combine like terms: -36.935044876 + 125.5555556 = 88.620510724 t = 88.620510724 Simplifying t = 88.620510724Solution
The solution to the problem is based on the solutions from the subproblems. t = {162.490600476, 88.620510724}
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