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Simplifying -0.921 = -2.57t + 0.5 * -9.8t2 Multiply 0.5 * -9.8 -0.921 = -2.57t + -4.9t2 Solving -0.921 = -2.57t + -4.9t2 Solving for variable 't'. Reorder the terms: -0.921 + 2.57t + 4.9t2 = -2.57t + 2.57t + -4.9t2 + 4.9t2 Combine like terms: -2.57t + 2.57t = 0.00 -0.921 + 2.57t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -0.921 + 2.57t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.921 + 2.57t + 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 + 0.5244897959t + t2 = 0 Move the constant term to the right: Add '0.1879591837' to each side of the equation. -0.1879591837 + 0.5244897959t + 0.1879591837 + t2 = 0 + 0.1879591837 Reorder the terms: -0.1879591837 + 0.1879591837 + 0.5244897959t + t2 = 0 + 0.1879591837 Combine like terms: -0.1879591837 + 0.1879591837 = 0.0000000000 0.0000000000 + 0.5244897959t + t2 = 0 + 0.1879591837 0.5244897959t + t2 = 0 + 0.1879591837 Combine like terms: 0 + 0.1879591837 = 0.1879591837 0.5244897959t + t2 = 0.1879591837 The t term is 0.5244897959t. Take half its coefficient (0.262244898). Square it (0.06877238653) and add it to both sides. Add '0.06877238653' to each side of the equation. 0.5244897959t + 0.06877238653 + t2 = 0.1879591837 + 0.06877238653 Reorder the terms: 0.06877238653 + 0.5244897959t + t2 = 0.1879591837 + 0.06877238653 Combine like terms: 0.1879591837 + 0.06877238653 = 0.25673157023 0.06877238653 + 0.5244897959t + t2 = 0.25673157023 Factor a perfect square on the left side: (t + 0.262244898)(t + 0.262244898) = 0.25673157023 Calculate the square root of the right side: 0.506686856 Break this problem into two subproblems by setting (t + 0.262244898) equal to 0.506686856 and -0.506686856.Subproblem 1
t + 0.262244898 = 0.506686856 Simplifying t + 0.262244898 = 0.506686856 Reorder the terms: 0.262244898 + t = 0.506686856 Solving 0.262244898 + t = 0.506686856 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.262244898' to each side of the equation. 0.262244898 + -0.262244898 + t = 0.506686856 + -0.262244898 Combine like terms: 0.262244898 + -0.262244898 = 0.000000000 0.000000000 + t = 0.506686856 + -0.262244898 t = 0.506686856 + -0.262244898 Combine like terms: 0.506686856 + -0.262244898 = 0.244441958 t = 0.244441958 Simplifying t = 0.244441958Subproblem 2
t + 0.262244898 = -0.506686856 Simplifying t + 0.262244898 = -0.506686856 Reorder the terms: 0.262244898 + t = -0.506686856 Solving 0.262244898 + t = -0.506686856 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.262244898' to each side of the equation. 0.262244898 + -0.262244898 + t = -0.506686856 + -0.262244898 Combine like terms: 0.262244898 + -0.262244898 = 0.000000000 0.000000000 + t = -0.506686856 + -0.262244898 t = -0.506686856 + -0.262244898 Combine like terms: -0.506686856 + -0.262244898 = -0.768931754 t = -0.768931754 Simplifying t = -0.768931754Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.244441958, -0.768931754}
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