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Simplifying (2t2 + -7t + -3) + (6t2 + -4t + 5) = 0 Reorder the terms: (-3 + -7t + 2t2) + (6t2 + -4t + 5) = 0 Remove parenthesis around (-3 + -7t + 2t2) -3 + -7t + 2t2 + (6t2 + -4t + 5) = 0 Reorder the terms: -3 + -7t + 2t2 + (5 + -4t + 6t2) = 0 Remove parenthesis around (5 + -4t + 6t2) -3 + -7t + 2t2 + 5 + -4t + 6t2 = 0 Reorder the terms: -3 + 5 + -7t + -4t + 2t2 + 6t2 = 0 Combine like terms: -3 + 5 = 2 2 + -7t + -4t + 2t2 + 6t2 = 0 Combine like terms: -7t + -4t = -11t 2 + -11t + 2t2 + 6t2 = 0 Combine like terms: 2t2 + 6t2 = 8t2 2 + -11t + 8t2 = 0 Solving 2 + -11t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -1.375t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.375t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.375t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.375t + t2 = 0 + -0.25 -1.375t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.375t + t2 = -0.25 The t term is -1.375t. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375t + 0.47265625 + t2 = -0.25 + 0.47265625 Reorder the terms: 0.47265625 + -1.375t + t2 = -0.25 + 0.47265625 Combine like terms: -0.25 + 0.47265625 = 0.22265625 0.47265625 + -1.375t + t2 = 0.22265625 Factor a perfect square on the left side: (t + -0.6875)(t + -0.6875) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (t + -0.6875) equal to 0.471864652 and -0.471864652.Subproblem 1
t + -0.6875 = 0.471864652 Simplifying t + -0.6875 = 0.471864652 Reorder the terms: -0.6875 + t = 0.471864652 Solving -0.6875 + t = 0.471864652 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + t = 0.471864652 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = 0.471864652 + 0.6875 t = 0.471864652 + 0.6875 Combine like terms: 0.471864652 + 0.6875 = 1.159364652 t = 1.159364652 Simplifying t = 1.159364652Subproblem 2
t + -0.6875 = -0.471864652 Simplifying t + -0.6875 = -0.471864652 Reorder the terms: -0.6875 + t = -0.471864652 Solving -0.6875 + t = -0.471864652 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + t = -0.471864652 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = -0.471864652 + 0.6875 t = -0.471864652 + 0.6875 Combine like terms: -0.471864652 + 0.6875 = 0.215635348 t = 0.215635348 Simplifying t = 0.215635348Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.159364652, 0.215635348}
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