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Simplifying 49t2 + 30t + -75 = 0 Reorder the terms: -75 + 30t + 49t2 = 0 Solving -75 + 30t + 49t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -1.530612245 + 0.612244898t + t2 = 0 Move the constant term to the right: Add '1.530612245' to each side of the equation. -1.530612245 + 0.612244898t + 1.530612245 + t2 = 0 + 1.530612245 Reorder the terms: -1.530612245 + 1.530612245 + 0.612244898t + t2 = 0 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + 0.612244898t + t2 = 0 + 1.530612245 0.612244898t + t2 = 0 + 1.530612245 Combine like terms: 0 + 1.530612245 = 1.530612245 0.612244898t + t2 = 1.530612245 The t term is 0.612244898t. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898t + 0.09371095378 + t2 = 1.530612245 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898t + t2 = 1.530612245 + 0.09371095378 Combine like terms: 1.530612245 + 0.09371095378 = 1.62432319878 0.09371095378 + 0.612244898t + t2 = 1.62432319878 Factor a perfect square on the left side: (t + 0.306122449)(t + 0.306122449) = 1.62432319878 Calculate the square root of the right side: 1.274489387 Break this problem into two subproblems by setting (t + 0.306122449) equal to 1.274489387 and -1.274489387.Subproblem 1
t + 0.306122449 = 1.274489387 Simplifying t + 0.306122449 = 1.274489387 Reorder the terms: 0.306122449 + t = 1.274489387 Solving 0.306122449 + t = 1.274489387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = 1.274489387 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = 1.274489387 + -0.306122449 t = 1.274489387 + -0.306122449 Combine like terms: 1.274489387 + -0.306122449 = 0.968366938 t = 0.968366938 Simplifying t = 0.968366938Subproblem 2
t + 0.306122449 = -1.274489387 Simplifying t + 0.306122449 = -1.274489387 Reorder the terms: 0.306122449 + t = -1.274489387 Solving 0.306122449 + t = -1.274489387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = -1.274489387 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = -1.274489387 + -0.306122449 t = -1.274489387 + -0.306122449 Combine like terms: -1.274489387 + -0.306122449 = -1.580611836 t = -1.580611836 Simplifying t = -1.580611836Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.968366938, -1.580611836}
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