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Simplifying 7t2 + -7t + 1 = 0 Reorder the terms: 1 + -7t + 7t2 = 0 Solving 1 + -7t + 7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -1t + t2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -1t + -0.1428571429 + t2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -1t + t2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -1t + t2 = 0 + -0.1428571429 -1t + t2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -1t + t2 = -0.1428571429 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = -0.1428571429 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -0.1428571429 + 0.25 Combine like terms: -0.1428571429 + 0.25 = 0.1071428571 0.25 + -1t + t2 = 0.1071428571 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.1071428571 Calculate the square root of the right side: 0.327326835 Break this problem into two subproblems by setting (t + -0.5) equal to 0.327326835 and -0.327326835.Subproblem 1
t + -0.5 = 0.327326835 Simplifying t + -0.5 = 0.327326835 Reorder the terms: -0.5 + t = 0.327326835 Solving -0.5 + t = 0.327326835 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.327326835 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.327326835 + 0.5 t = 0.327326835 + 0.5 Combine like terms: 0.327326835 + 0.5 = 0.827326835 t = 0.827326835 Simplifying t = 0.827326835Subproblem 2
t + -0.5 = -0.327326835 Simplifying t + -0.5 = -0.327326835 Reorder the terms: -0.5 + t = -0.327326835 Solving -0.5 + t = -0.327326835 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.327326835 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.327326835 + 0.5 t = -0.327326835 + 0.5 Combine like terms: -0.327326835 + 0.5 = 0.172673165 t = 0.172673165 Simplifying t = 0.172673165Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.827326835, 0.172673165}
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