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Simplifying 4.9t2 + -17t + 3.8 = 0 Reorder the terms: 3.8 + -17t + 4.9t2 = 0 Solving 3.8 + -17t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.7755102041 + -3.469387755t + t2 = 0 Move the constant term to the right: Add '-0.7755102041' to each side of the equation. 0.7755102041 + -3.469387755t + -0.7755102041 + t2 = 0 + -0.7755102041 Reorder the terms: 0.7755102041 + -0.7755102041 + -3.469387755t + t2 = 0 + -0.7755102041 Combine like terms: 0.7755102041 + -0.7755102041 = 0.0000000000 0.0000000000 + -3.469387755t + t2 = 0 + -0.7755102041 -3.469387755t + t2 = 0 + -0.7755102041 Combine like terms: 0 + -0.7755102041 = -0.7755102041 -3.469387755t + t2 = -0.7755102041 The t term is -3.469387755t. Take half its coefficient (-1.734693878). Square it (3.009162850) and add it to both sides. Add '3.009162850' to each side of the equation. -3.469387755t + 3.009162850 + t2 = -0.7755102041 + 3.009162850 Reorder the terms: 3.009162850 + -3.469387755t + t2 = -0.7755102041 + 3.009162850 Combine like terms: -0.7755102041 + 3.009162850 = 2.2336526459 3.009162850 + -3.469387755t + t2 = 2.2336526459 Factor a perfect square on the left side: (t + -1.734693878)(t + -1.734693878) = 2.2336526459 Calculate the square root of the right side: 1.494540948 Break this problem into two subproblems by setting (t + -1.734693878) equal to 1.494540948 and -1.494540948.Subproblem 1
t + -1.734693878 = 1.494540948 Simplifying t + -1.734693878 = 1.494540948 Reorder the terms: -1.734693878 + t = 1.494540948 Solving -1.734693878 + t = 1.494540948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + t = 1.494540948 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + t = 1.494540948 + 1.734693878 t = 1.494540948 + 1.734693878 Combine like terms: 1.494540948 + 1.734693878 = 3.229234826 t = 3.229234826 Simplifying t = 3.229234826Subproblem 2
t + -1.734693878 = -1.494540948 Simplifying t + -1.734693878 = -1.494540948 Reorder the terms: -1.734693878 + t = -1.494540948 Solving -1.734693878 + t = -1.494540948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + t = -1.494540948 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + t = -1.494540948 + 1.734693878 t = -1.494540948 + 1.734693878 Combine like terms: -1.494540948 + 1.734693878 = 0.24015293 t = 0.24015293 Simplifying t = 0.24015293Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.229234826, 0.24015293}
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