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Simplifying -21.1 = 13.0t + 0.5(-9.8) * t2 Multiply 0.5 * -9.8 -21.1 = 13.0t + -4.9t2 Solving -21.1 = 13.0t + -4.9t2 Solving for variable 't'. Reorder the terms: -21.1 + -13.0t + 4.9t2 = 13.0t + -13.0t + -4.9t2 + 4.9t2 Combine like terms: 13.0t + -13.0t = 0.0 -21.1 + -13.0t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -21.1 + -13.0t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -21.1 + -13.0t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.306122449 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '4.306122449' to each side of the equation. -4.306122449 + -2.653061224t + 4.306122449 + t2 = 0 + 4.306122449 Reorder the terms: -4.306122449 + 4.306122449 + -2.653061224t + t2 = 0 + 4.306122449 Combine like terms: -4.306122449 + 4.306122449 = 0.000000000 0.000000000 + -2.653061224t + t2 = 0 + 4.306122449 -2.653061224t + t2 = 0 + 4.306122449 Combine like terms: 0 + 4.306122449 = 4.306122449 -2.653061224t + t2 = 4.306122449 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 = 4.306122449 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = 4.306122449 + 1.759683465 Combine like terms: 4.306122449 + 1.759683465 = 6.065805914 1.759683465 + -2.653061224t + t2 = 6.065805914 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 6.065805914 Calculate the square root of the right side: 2.462885688 Break this problem into two subproblems by setting (t + -1.326530612) equal to 2.462885688 and -2.462885688.Subproblem 1
t + -1.326530612 = 2.462885688 Simplifying t + -1.326530612 = 2.462885688 Reorder the terms: -1.326530612 + t = 2.462885688 Solving -1.326530612 + t = 2.462885688 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 = 2.462885688 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 2.462885688 + 1.326530612 t = 2.462885688 + 1.326530612 Combine like terms: 2.462885688 + 1.326530612 = 3.7894163 t = 3.7894163 Simplifying t = 3.7894163Subproblem 2
t + -1.326530612 = -2.462885688 Simplifying t + -1.326530612 = -2.462885688 Reorder the terms: -1.326530612 + t = -2.462885688 Solving -1.326530612 + t = -2.462885688 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 = -2.462885688 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -2.462885688 + 1.326530612 t = -2.462885688 + 1.326530612 Combine like terms: -2.462885688 + 1.326530612 = -1.136355076 t = -1.136355076 Simplifying t = -1.136355076Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.7894163, -1.136355076}
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