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Simplifying -0.921 = 3.78t + 0.5 * -9.8t2 Multiply 0.5 * -9.8 -0.921 = 3.78t + -4.9t2 Solving -0.921 = 3.78t + -4.9t2 Solving for variable 't'. Reorder the terms: -0.921 + -3.78t + 4.9t2 = 3.78t + -3.78t + -4.9t2 + 4.9t2 Combine like terms: 3.78t + -3.78t = 0.00 -0.921 + -3.78t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -0.921 + -3.78t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.921 + -3.78t + 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'. -0.1879591837 + -0.7714285714t + t2 = 0 Move the constant term to the right: Add '0.1879591837' to each side of the equation. -0.1879591837 + -0.7714285714t + 0.1879591837 + t2 = 0 + 0.1879591837 Reorder the terms: -0.1879591837 + 0.1879591837 + -0.7714285714t + t2 = 0 + 0.1879591837 Combine like terms: -0.1879591837 + 0.1879591837 = 0.0000000000 0.0000000000 + -0.7714285714t + t2 = 0 + 0.1879591837 -0.7714285714t + t2 = 0 + 0.1879591837 Combine like terms: 0 + 0.1879591837 = 0.1879591837 -0.7714285714t + t2 = 0.1879591837 The t term is -0.7714285714t. Take half its coefficient (-0.3857142857). Square it (0.1487755102) and add it to both sides. Add '0.1487755102' to each side of the equation. -0.7714285714t + 0.1487755102 + t2 = 0.1879591837 + 0.1487755102 Reorder the terms: 0.1487755102 + -0.7714285714t + t2 = 0.1879591837 + 0.1487755102 Combine like terms: 0.1879591837 + 0.1487755102 = 0.3367346939 0.1487755102 + -0.7714285714t + t2 = 0.3367346939 Factor a perfect square on the left side: (t + -0.3857142857)(t + -0.3857142857) = 0.3367346939 Calculate the square root of the right side: 0.580288457 Break this problem into two subproblems by setting (t + -0.3857142857) equal to 0.580288457 and -0.580288457.Subproblem 1
t + -0.3857142857 = 0.580288457 Simplifying t + -0.3857142857 = 0.580288457 Reorder the terms: -0.3857142857 + t = 0.580288457 Solving -0.3857142857 + t = 0.580288457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3857142857' to each side of the equation. -0.3857142857 + 0.3857142857 + t = 0.580288457 + 0.3857142857 Combine like terms: -0.3857142857 + 0.3857142857 = 0.0000000000 0.0000000000 + t = 0.580288457 + 0.3857142857 t = 0.580288457 + 0.3857142857 Combine like terms: 0.580288457 + 0.3857142857 = 0.9660027427 t = 0.9660027427 Simplifying t = 0.9660027427Subproblem 2
t + -0.3857142857 = -0.580288457 Simplifying t + -0.3857142857 = -0.580288457 Reorder the terms: -0.3857142857 + t = -0.580288457 Solving -0.3857142857 + t = -0.580288457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3857142857' to each side of the equation. -0.3857142857 + 0.3857142857 + t = -0.580288457 + 0.3857142857 Combine like terms: -0.3857142857 + 0.3857142857 = 0.0000000000 0.0000000000 + t = -0.580288457 + 0.3857142857 t = -0.580288457 + 0.3857142857 Combine like terms: -0.580288457 + 0.3857142857 = -0.1945741713 t = -0.1945741713 Simplifying t = -0.1945741713Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.9660027427, -0.1945741713}
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