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Simplifying 5t2 + -13t + 7 = 0 Reorder the terms: 7 + -13t + 5t2 = 0 Solving 7 + -13t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -2.6t + t2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -2.6t + -1.4 + t2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -2.6t + t2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -2.6t + t2 = 0 + -1.4 -2.6t + t2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -2.6t + t2 = -1.4 The t term is -2.6t. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6t + 1.69 + t2 = -1.4 + 1.69 Reorder the terms: 1.69 + -2.6t + t2 = -1.4 + 1.69 Combine like terms: -1.4 + 1.69 = 0.29 1.69 + -2.6t + t2 = 0.29 Factor a perfect square on the left side: (t + -1.3)(t + -1.3) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (t + -1.3) equal to 0.538516481 and -0.538516481.Subproblem 1
t + -1.3 = 0.538516481 Simplifying t + -1.3 = 0.538516481 Reorder the terms: -1.3 + t = 0.538516481 Solving -1.3 + t = 0.538516481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = 0.538516481 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = 0.538516481 + 1.3 t = 0.538516481 + 1.3 Combine like terms: 0.538516481 + 1.3 = 1.838516481 t = 1.838516481 Simplifying t = 1.838516481Subproblem 2
t + -1.3 = -0.538516481 Simplifying t + -1.3 = -0.538516481 Reorder the terms: -1.3 + t = -0.538516481 Solving -1.3 + t = -0.538516481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = -0.538516481 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = -0.538516481 + 1.3 t = -0.538516481 + 1.3 Combine like terms: -0.538516481 + 1.3 = 0.761483519 t = 0.761483519 Simplifying t = 0.761483519Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.838516481, 0.761483519}
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