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Simplifying -4.9t2 + 13t + 1 = 0 Reorder the terms: 1 + 13t + -4.9t2 = 0 Solving 1 + 13t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.2040816327 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -2.653061224t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -2.653061224t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -2.653061224t + t2 = 0 + 0.2040816327 -2.653061224t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -2.653061224t + t2 = 0.2040816327 The t term is -2.653061224t. Take half its coefficient (-1.326530612). Square it (1.759683465) and add it to both sides. Add '1.759683465' to each side of the equation. -2.653061224t + 1.759683465 + t2 = 0.2040816327 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = 0.2040816327 + 1.759683465 Combine like terms: 0.2040816327 + 1.759683465 = 1.9637650977 1.759683465 + -2.653061224t + t2 = 1.9637650977 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 1.9637650977 Calculate the square root of the right side: 1.401344033 Break this problem into two subproblems by setting (t + -1.326530612) equal to 1.401344033 and -1.401344033.Subproblem 1
t + -1.326530612 = 1.401344033 Simplifying t + -1.326530612 = 1.401344033 Reorder the terms: -1.326530612 + t = 1.401344033 Solving -1.326530612 + t = 1.401344033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + t = 1.401344033 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 1.401344033 + 1.326530612 t = 1.401344033 + 1.326530612 Combine like terms: 1.401344033 + 1.326530612 = 2.727874645 t = 2.727874645 Simplifying t = 2.727874645Subproblem 2
t + -1.326530612 = -1.401344033 Simplifying t + -1.326530612 = -1.401344033 Reorder the terms: -1.326530612 + t = -1.401344033 Solving -1.326530612 + t = -1.401344033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + t = -1.401344033 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -1.401344033 + 1.326530612 t = -1.401344033 + 1.326530612 Combine like terms: -1.401344033 + 1.326530612 = -0.074813421 t = -0.074813421 Simplifying t = -0.074813421Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.727874645, -0.074813421}
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