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Simplifying 0 = 141 + 5.98t + -4.9t2 Solving 0 = 141 + 5.98t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -141 = -141 -141 + -5.98t + 4.9t2 = 141 + 5.98t + -4.9t2 + -141 + -5.98t + 4.9t2 Reorder the terms: -141 + -5.98t + 4.9t2 = 141 + -141 + 5.98t + -5.98t + -4.9t2 + 4.9t2 Combine like terms: 141 + -141 = 0 -141 + -5.98t + 4.9t2 = 0 + 5.98t + -5.98t + -4.9t2 + 4.9t2 -141 + -5.98t + 4.9t2 = 5.98t + -5.98t + -4.9t2 + 4.9t2 Combine like terms: 5.98t + -5.98t = 0.00 -141 + -5.98t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -141 + -5.98t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -141 + -5.98t + 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'. -28.7755102 + -1.220408163t + t2 = 0 Move the constant term to the right: Add '28.7755102' to each side of the equation. -28.7755102 + -1.220408163t + 28.7755102 + t2 = 0 + 28.7755102 Reorder the terms: -28.7755102 + 28.7755102 + -1.220408163t + t2 = 0 + 28.7755102 Combine like terms: -28.7755102 + 28.7755102 = 0.0000000 0.0000000 + -1.220408163t + t2 = 0 + 28.7755102 -1.220408163t + t2 = 0 + 28.7755102 Combine like terms: 0 + 28.7755102 = 28.7755102 -1.220408163t + t2 = 28.7755102 The t term is -1.220408163t. Take half its coefficient (-0.6102040815). Square it (0.3723490211) and add it to both sides. Add '0.3723490211' to each side of the equation. -1.220408163t + 0.3723490211 + t2 = 28.7755102 + 0.3723490211 Reorder the terms: 0.3723490211 + -1.220408163t + t2 = 28.7755102 + 0.3723490211 Combine like terms: 28.7755102 + 0.3723490211 = 29.1478592211 0.3723490211 + -1.220408163t + t2 = 29.1478592211 Factor a perfect square on the left side: (t + -0.6102040815)(t + -0.6102040815) = 29.1478592211 Calculate the square root of the right side: 5.398875737 Break this problem into two subproblems by setting (t + -0.6102040815) equal to 5.398875737 and -5.398875737.Subproblem 1
t + -0.6102040815 = 5.398875737 Simplifying t + -0.6102040815 = 5.398875737 Reorder the terms: -0.6102040815 + t = 5.398875737 Solving -0.6102040815 + t = 5.398875737 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6102040815' to each side of the equation. -0.6102040815 + 0.6102040815 + t = 5.398875737 + 0.6102040815 Combine like terms: -0.6102040815 + 0.6102040815 = 0.0000000000 0.0000000000 + t = 5.398875737 + 0.6102040815 t = 5.398875737 + 0.6102040815 Combine like terms: 5.398875737 + 0.6102040815 = 6.0090798185 t = 6.0090798185 Simplifying t = 6.0090798185Subproblem 2
t + -0.6102040815 = -5.398875737 Simplifying t + -0.6102040815 = -5.398875737 Reorder the terms: -0.6102040815 + t = -5.398875737 Solving -0.6102040815 + t = -5.398875737 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6102040815' to each side of the equation. -0.6102040815 + 0.6102040815 + t = -5.398875737 + 0.6102040815 Combine like terms: -0.6102040815 + 0.6102040815 = 0.0000000000 0.0000000000 + t = -5.398875737 + 0.6102040815 t = -5.398875737 + 0.6102040815 Combine like terms: -5.398875737 + 0.6102040815 = -4.7886716555 t = -4.7886716555 Simplifying t = -4.7886716555Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.0090798185, -4.7886716555}
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