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Simplifying 0 = -4.9t2 + -3t + 950 Reorder the terms: 0 = 950 + -3t + -4.9t2 Solving 0 = 950 + -3t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -950 = -950 -950 + 3t + 4.9t2 = 950 + -3t + -4.9t2 + -950 + 3t + 4.9t2 Reorder the terms: -950 + 3t + 4.9t2 = 950 + -950 + -3t + 3t + -4.9t2 + 4.9t2 Combine like terms: 950 + -950 = 0 -950 + 3t + 4.9t2 = 0 + -3t + 3t + -4.9t2 + 4.9t2 -950 + 3t + 4.9t2 = -3t + 3t + -4.9t2 + 4.9t2 Combine like terms: -3t + 3t = 0 -950 + 3t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -950 + 3t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -950 + 3t + 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'. -193.877551 + 0.612244898t + t2 = 0 Move the constant term to the right: Add '193.877551' to each side of the equation. -193.877551 + 0.612244898t + 193.877551 + t2 = 0 + 193.877551 Reorder the terms: -193.877551 + 193.877551 + 0.612244898t + t2 = 0 + 193.877551 Combine like terms: -193.877551 + 193.877551 = 0.000000 0.000000 + 0.612244898t + t2 = 0 + 193.877551 0.612244898t + t2 = 0 + 193.877551 Combine like terms: 0 + 193.877551 = 193.877551 0.612244898t + t2 = 193.877551 The t term is 0.612244898t. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898t + 0.09371095378 + t2 = 193.877551 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898t + t2 = 193.877551 + 0.09371095378 Combine like terms: 193.877551 + 0.09371095378 = 193.97126195378 0.09371095378 + 0.612244898t + t2 = 193.97126195378 Factor a perfect square on the left side: (t + 0.306122449)(t + 0.306122449) = 193.97126195378 Calculate the square root of the right side: 13.927356603 Break this problem into two subproblems by setting (t + 0.306122449) equal to 13.927356603 and -13.927356603.Subproblem 1
t + 0.306122449 = 13.927356603 Simplifying t + 0.306122449 = 13.927356603 Reorder the terms: 0.306122449 + t = 13.927356603 Solving 0.306122449 + t = 13.927356603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = 13.927356603 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = 13.927356603 + -0.306122449 t = 13.927356603 + -0.306122449 Combine like terms: 13.927356603 + -0.306122449 = 13.621234154 t = 13.621234154 Simplifying t = 13.621234154Subproblem 2
t + 0.306122449 = -13.927356603 Simplifying t + 0.306122449 = -13.927356603 Reorder the terms: 0.306122449 + t = -13.927356603 Solving 0.306122449 + t = -13.927356603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = -13.927356603 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = -13.927356603 + -0.306122449 t = -13.927356603 + -0.306122449 Combine like terms: -13.927356603 + -0.306122449 = -14.233479052 t = -14.233479052 Simplifying t = -14.233479052Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.621234154, -14.233479052}
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