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Simplifying 4.9t2 + -13t + -64 = 0 Reorder the terms: -64 + -13t + 4.9t2 = 0 Solving -64 + -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'. -13.06122449 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '13.06122449' to each side of the equation. -13.06122449 + -2.653061224t + 13.06122449 + t2 = 0 + 13.06122449 Reorder the terms: -13.06122449 + 13.06122449 + -2.653061224t + t2 = 0 + 13.06122449 Combine like terms: -13.06122449 + 13.06122449 = 0.00000000 0.00000000 + -2.653061224t + t2 = 0 + 13.06122449 -2.653061224t + t2 = 0 + 13.06122449 Combine like terms: 0 + 13.06122449 = 13.06122449 -2.653061224t + t2 = 13.06122449 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 = 13.06122449 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = 13.06122449 + 1.759683465 Combine like terms: 13.06122449 + 1.759683465 = 14.820907955 1.759683465 + -2.653061224t + t2 = 14.820907955 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 14.820907955 Calculate the square root of the right side: 3.849793235 Break this problem into two subproblems by setting (t + -1.326530612) equal to 3.849793235 and -3.849793235.Subproblem 1
t + -1.326530612 = 3.849793235 Simplifying t + -1.326530612 = 3.849793235 Reorder the terms: -1.326530612 + t = 3.849793235 Solving -1.326530612 + t = 3.849793235 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 = 3.849793235 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 3.849793235 + 1.326530612 t = 3.849793235 + 1.326530612 Combine like terms: 3.849793235 + 1.326530612 = 5.176323847 t = 5.176323847 Simplifying t = 5.176323847Subproblem 2
t + -1.326530612 = -3.849793235 Simplifying t + -1.326530612 = -3.849793235 Reorder the terms: -1.326530612 + t = -3.849793235 Solving -1.326530612 + t = -3.849793235 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 = -3.849793235 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -3.849793235 + 1.326530612 t = -3.849793235 + 1.326530612 Combine like terms: -3.849793235 + 1.326530612 = -2.523262623 t = -2.523262623 Simplifying t = -2.523262623Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.176323847, -2.523262623}
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