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Simplifying -1t(5t + -7) = -5 Reorder the terms: -1t(-7 + 5t) = -5 (-7 * -1t + 5t * -1t) = -5 (7t + -5t2) = -5 Solving 7t + -5t2 = -5 Solving for variable 't'. Reorder the terms: 5 + 7t + -5t2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 7t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1 + -1.4t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.4t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -1.4t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.4t + t2 = 0 + 1 -1.4t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.4t + t2 = 1 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 = 1 + 0.49 Reorder the terms: 0.49 + -1.4t + t2 = 1 + 0.49 Combine like terms: 1 + 0.49 = 1.49 0.49 + -1.4t + t2 = 1.49 Factor a perfect square on the left side: (t + -0.7)(t + -0.7) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (t + -0.7) equal to 1.220655562 and -1.220655562.Subproblem 1
t + -0.7 = 1.220655562 Simplifying t + -0.7 = 1.220655562 Reorder the terms: -0.7 + t = 1.220655562 Solving -0.7 + t = 1.220655562 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 = 1.220655562 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 1.220655562 + 0.7 t = 1.220655562 + 0.7 Combine like terms: 1.220655562 + 0.7 = 1.920655562 t = 1.920655562 Simplifying t = 1.920655562Subproblem 2
t + -0.7 = -1.220655562 Simplifying t + -0.7 = -1.220655562 Reorder the terms: -0.7 + t = -1.220655562 Solving -0.7 + t = -1.220655562 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 = -1.220655562 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -1.220655562 + 0.7 t = -1.220655562 + 0.7 Combine like terms: -1.220655562 + 0.7 = -0.520655562 t = -0.520655562 Simplifying t = -0.520655562Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.920655562, -0.520655562}
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