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Simplifying 4.905t2 + -11.8t + -2.4 = 0 Reorder the terms: -2.4 + -11.8t + 4.905t2 = 0 Solving -2.4 + -11.8t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -0.4892966361 + -2.405708461t + t2 = 0 Move the constant term to the right: Add '0.4892966361' to each side of the equation. -0.4892966361 + -2.405708461t + 0.4892966361 + t2 = 0 + 0.4892966361 Reorder the terms: -0.4892966361 + 0.4892966361 + -2.405708461t + t2 = 0 + 0.4892966361 Combine like terms: -0.4892966361 + 0.4892966361 = 0.0000000000 0.0000000000 + -2.405708461t + t2 = 0 + 0.4892966361 -2.405708461t + t2 = 0 + 0.4892966361 Combine like terms: 0 + 0.4892966361 = 0.4892966361 -2.405708461t + t2 = 0.4892966361 The t term is -2.405708461t. Take half its coefficient (-1.202854231). Square it (1.446858301) and add it to both sides. Add '1.446858301' to each side of the equation. -2.405708461t + 1.446858301 + t2 = 0.4892966361 + 1.446858301 Reorder the terms: 1.446858301 + -2.405708461t + t2 = 0.4892966361 + 1.446858301 Combine like terms: 0.4892966361 + 1.446858301 = 1.9361549371 1.446858301 + -2.405708461t + t2 = 1.9361549371 Factor a perfect square on the left side: (t + -1.202854231)(t + -1.202854231) = 1.9361549371 Calculate the square root of the right side: 1.391457846 Break this problem into two subproblems by setting (t + -1.202854231) equal to 1.391457846 and -1.391457846.Subproblem 1
t + -1.202854231 = 1.391457846 Simplifying t + -1.202854231 = 1.391457846 Reorder the terms: -1.202854231 + t = 1.391457846 Solving -1.202854231 + t = 1.391457846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.202854231' to each side of the equation. -1.202854231 + 1.202854231 + t = 1.391457846 + 1.202854231 Combine like terms: -1.202854231 + 1.202854231 = 0.000000000 0.000000000 + t = 1.391457846 + 1.202854231 t = 1.391457846 + 1.202854231 Combine like terms: 1.391457846 + 1.202854231 = 2.594312077 t = 2.594312077 Simplifying t = 2.594312077Subproblem 2
t + -1.202854231 = -1.391457846 Simplifying t + -1.202854231 = -1.391457846 Reorder the terms: -1.202854231 + t = -1.391457846 Solving -1.202854231 + t = -1.391457846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.202854231' to each side of the equation. -1.202854231 + 1.202854231 + t = -1.391457846 + 1.202854231 Combine like terms: -1.202854231 + 1.202854231 = 0.000000000 0.000000000 + t = -1.391457846 + 1.202854231 t = -1.391457846 + 1.202854231 Combine like terms: -1.391457846 + 1.202854231 = -0.188603615 t = -0.188603615 Simplifying t = -0.188603615Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.594312077, -0.188603615}
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