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Simplifying 7t = 5t2 + 1 Reorder the terms: 7t = 1 + 5t2 Solving 7t = 1 + 5t2 Solving for variable 't'. Reorder the terms: -1 + 7t + -5t2 = 1 + 5t2 + -1 + -5t2 Reorder the terms: -1 + 7t + -5t2 = 1 + -1 + 5t2 + -5t2 Combine like terms: 1 + -1 = 0 -1 + 7t + -5t2 = 0 + 5t2 + -5t2 -1 + 7t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 -1 + 7t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.2 + -1.4t + t2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.4t + -0.2 + t2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.4t + t2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.4t + t2 = 0 + -0.2 -1.4t + t2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.4t + t2 = -0.2 The t term is -1.4t. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4t + 0.49 + t2 = -0.2 + 0.49 Reorder the terms: 0.49 + -1.4t + t2 = -0.2 + 0.49 Combine like terms: -0.2 + 0.49 = 0.29 0.49 + -1.4t + t2 = 0.29 Factor a perfect square on the left side: (t + -0.7)(t + -0.7) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (t + -0.7) equal to 0.538516481 and -0.538516481.Subproblem 1
t + -0.7 = 0.538516481 Simplifying t + -0.7 = 0.538516481 Reorder the terms: -0.7 + t = 0.538516481 Solving -0.7 + t = 0.538516481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = 0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 0.538516481 + 0.7 t = 0.538516481 + 0.7 Combine like terms: 0.538516481 + 0.7 = 1.238516481 t = 1.238516481 Simplifying t = 1.238516481Subproblem 2
t + -0.7 = -0.538516481 Simplifying t + -0.7 = -0.538516481 Reorder the terms: -0.7 + t = -0.538516481 Solving -0.7 + t = -0.538516481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = -0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -0.538516481 + 0.7 t = -0.538516481 + 0.7 Combine like terms: -0.538516481 + 0.7 = 0.161483519 t = 0.161483519 Simplifying t = 0.161483519Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.238516481, 0.161483519}
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