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Simplifying 300t + -5t * t = 1 Multiply t * t 300t + -5t2 = 1 Solving 300t + -5t2 = 1 Solving for variable 't'. Reorder the terms: -1 + 300t + -5t2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 300t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.2 + -60t + t2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -60t + -0.2 + t2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -60t + t2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -60t + t2 = 0 + -0.2 -60t + t2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -60t + t2 = -0.2 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 = -0.2 + 900 Reorder the terms: 900 + -60t + t2 = -0.2 + 900 Combine like terms: -0.2 + 900 = 899.8 900 + -60t + t2 = 899.8 Factor a perfect square on the left side: (t + -30)(t + -30) = 899.8 Calculate the square root of the right side: 29.996666481 Break this problem into two subproblems by setting (t + -30) equal to 29.996666481 and -29.996666481.Subproblem 1
t + -30 = 29.996666481 Simplifying t + -30 = 29.996666481 Reorder the terms: -30 + t = 29.996666481 Solving -30 + t = 29.996666481 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 = 29.996666481 + 30 Combine like terms: -30 + 30 = 0 0 + t = 29.996666481 + 30 t = 29.996666481 + 30 Combine like terms: 29.996666481 + 30 = 59.996666481 t = 59.996666481 Simplifying t = 59.996666481Subproblem 2
t + -30 = -29.996666481 Simplifying t + -30 = -29.996666481 Reorder the terms: -30 + t = -29.996666481 Solving -30 + t = -29.996666481 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 = -29.996666481 + 30 Combine like terms: -30 + 30 = 0 0 + t = -29.996666481 + 30 t = -29.996666481 + 30 Combine like terms: -29.996666481 + 30 = 0.003333519 t = 0.003333519 Simplifying t = 0.003333519Solution
The solution to the problem is based on the solutions from the subproblems. t = {59.996666481, 0.003333519}
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