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Simplifying 245 = 99.8t + -5t2 Solving 245 = 99.8t + -5t2 Solving for variable 't'. Reorder the terms: 245 + -99.8t + 5t2 = 99.8t + -99.8t + -5t2 + 5t2 Combine like terms: 99.8t + -99.8t = 0.0 245 + -99.8t + 5t2 = 0.0 + -5t2 + 5t2 245 + -99.8t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 245 + -99.8t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 49 + -19.96t + t2 = 0 Move the constant term to the right: Add '-49' to each side of the equation. 49 + -19.96t + -49 + t2 = 0 + -49 Reorder the terms: 49 + -49 + -19.96t + t2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -19.96t + t2 = 0 + -49 -19.96t + t2 = 0 + -49 Combine like terms: 0 + -49 = -49 -19.96t + t2 = -49 The t term is -19.96t. Take half its coefficient (-9.98). Square it (99.6004) and add it to both sides. Add '99.6004' to each side of the equation. -19.96t + 99.6004 + t2 = -49 + 99.6004 Reorder the terms: 99.6004 + -19.96t + t2 = -49 + 99.6004 Combine like terms: -49 + 99.6004 = 50.6004 99.6004 + -19.96t + t2 = 50.6004 Factor a perfect square on the left side: (t + -9.98)(t + -9.98) = 50.6004 Calculate the square root of the right side: 7.113395814 Break this problem into two subproblems by setting (t + -9.98) equal to 7.113395814 and -7.113395814.Subproblem 1
t + -9.98 = 7.113395814 Simplifying t + -9.98 = 7.113395814 Reorder the terms: -9.98 + t = 7.113395814 Solving -9.98 + t = 7.113395814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.98' to each side of the equation. -9.98 + 9.98 + t = 7.113395814 + 9.98 Combine like terms: -9.98 + 9.98 = 0.00 0.00 + t = 7.113395814 + 9.98 t = 7.113395814 + 9.98 Combine like terms: 7.113395814 + 9.98 = 17.093395814 t = 17.093395814 Simplifying t = 17.093395814Subproblem 2
t + -9.98 = -7.113395814 Simplifying t + -9.98 = -7.113395814 Reorder the terms: -9.98 + t = -7.113395814 Solving -9.98 + t = -7.113395814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.98' to each side of the equation. -9.98 + 9.98 + t = -7.113395814 + 9.98 Combine like terms: -9.98 + 9.98 = 0.00 0.00 + t = -7.113395814 + 9.98 t = -7.113395814 + 9.98 Combine like terms: -7.113395814 + 9.98 = 2.866604186 t = 2.866604186 Simplifying t = 2.866604186Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.093395814, 2.866604186}
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