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Simplifying 4.9t2 + -13t + -24 = 0 Reorder the terms: -24 + -13t + 4.9t2 = 0 Solving -24 + -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'. -4.897959184 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '4.897959184' to each side of the equation. -4.897959184 + -2.653061224t + 4.897959184 + t2 = 0 + 4.897959184 Reorder the terms: -4.897959184 + 4.897959184 + -2.653061224t + t2 = 0 + 4.897959184 Combine like terms: -4.897959184 + 4.897959184 = 0.000000000 0.000000000 + -2.653061224t + t2 = 0 + 4.897959184 -2.653061224t + t2 = 0 + 4.897959184 Combine like terms: 0 + 4.897959184 = 4.897959184 -2.653061224t + t2 = 4.897959184 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 = 4.897959184 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = 4.897959184 + 1.759683465 Combine like terms: 4.897959184 + 1.759683465 = 6.657642649 1.759683465 + -2.653061224t + t2 = 6.657642649 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 6.657642649 Calculate the square root of the right side: 2.580240812 Break this problem into two subproblems by setting (t + -1.326530612) equal to 2.580240812 and -2.580240812.Subproblem 1
t + -1.326530612 = 2.580240812 Simplifying t + -1.326530612 = 2.580240812 Reorder the terms: -1.326530612 + t = 2.580240812 Solving -1.326530612 + t = 2.580240812 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 = 2.580240812 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 2.580240812 + 1.326530612 t = 2.580240812 + 1.326530612 Combine like terms: 2.580240812 + 1.326530612 = 3.906771424 t = 3.906771424 Simplifying t = 3.906771424Subproblem 2
t + -1.326530612 = -2.580240812 Simplifying t + -1.326530612 = -2.580240812 Reorder the terms: -1.326530612 + t = -2.580240812 Solving -1.326530612 + t = -2.580240812 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 = -2.580240812 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -2.580240812 + 1.326530612 t = -2.580240812 + 1.326530612 Combine like terms: -2.580240812 + 1.326530612 = -1.2537102 t = -1.2537102 Simplifying t = -1.2537102Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.906771424, -1.2537102}
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