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Simplifying 1.75t2 + -4t + 1 = 0 Reorder the terms: 1 + -4t + 1.75t2 = 0 Solving 1 + -4t + 1.75t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. 0.5714285714 + -2.285714286t + t2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -2.285714286t + -0.5714285714 + t2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -2.285714286t + t2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -2.285714286t + t2 = 0 + -0.5714285714 -2.285714286t + t2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -2.285714286t + t2 = -0.5714285714 The t term is -2.285714286t. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286t + 1.306122449 + t2 = -0.5714285714 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286t + t2 = -0.5714285714 + 1.306122449 Combine like terms: -0.5714285714 + 1.306122449 = 0.7346938776 1.306122449 + -2.285714286t + t2 = 0.7346938776 Factor a perfect square on the left side: (t + -1.142857143)(t + -1.142857143) = 0.7346938776 Calculate the square root of the right side: 0.857142857 Break this problem into two subproblems by setting (t + -1.142857143) equal to 0.857142857 and -0.857142857.Subproblem 1
t + -1.142857143 = 0.857142857 Simplifying t + -1.142857143 = 0.857142857 Reorder the terms: -1.142857143 + t = 0.857142857 Solving -1.142857143 + t = 0.857142857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + t = 0.857142857 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + t = 0.857142857 + 1.142857143 t = 0.857142857 + 1.142857143 Combine like terms: 0.857142857 + 1.142857143 = 2 t = 2 Simplifying t = 2Subproblem 2
t + -1.142857143 = -0.857142857 Simplifying t + -1.142857143 = -0.857142857 Reorder the terms: -1.142857143 + t = -0.857142857 Solving -1.142857143 + t = -0.857142857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + t = -0.857142857 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + t = -0.857142857 + 1.142857143 t = -0.857142857 + 1.142857143 Combine like terms: -0.857142857 + 1.142857143 = 0.285714286 t = 0.285714286 Simplifying t = 0.285714286Solution
The solution to the problem is based on the solutions from the subproblems. t = {2, 0.285714286}
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