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Simplifying 200 = -4.9t2 + 86t + 2.1 Reorder the terms: 200 = 2.1 + 86t + -4.9t2 Solving 200 = 2.1 + 86t + -4.9t2 Solving for variable 't'. Combine like terms: 200 + -2.1 = 197.9 197.9 + -86t + 4.9t2 = 2.1 + 86t + -4.9t2 + -2.1 + -86t + 4.9t2 Reorder the terms: 197.9 + -86t + 4.9t2 = 2.1 + -2.1 + 86t + -86t + -4.9t2 + 4.9t2 Combine like terms: 2.1 + -2.1 = 0.0 197.9 + -86t + 4.9t2 = 0.0 + 86t + -86t + -4.9t2 + 4.9t2 197.9 + -86t + 4.9t2 = 86t + -86t + -4.9t2 + 4.9t2 Combine like terms: 86t + -86t = 0 197.9 + -86t + 4.9t2 = 0 + -4.9t2 + 4.9t2 197.9 + -86t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 197.9 + -86t + 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'. 40.3877551 + -17.55102041t + t2 = 0 Move the constant term to the right: Add '-40.3877551' to each side of the equation. 40.3877551 + -17.55102041t + -40.3877551 + t2 = 0 + -40.3877551 Reorder the terms: 40.3877551 + -40.3877551 + -17.55102041t + t2 = 0 + -40.3877551 Combine like terms: 40.3877551 + -40.3877551 = 0.0000000 0.0000000 + -17.55102041t + t2 = 0 + -40.3877551 -17.55102041t + t2 = 0 + -40.3877551 Combine like terms: 0 + -40.3877551 = -40.3877551 -17.55102041t + t2 = -40.3877551 The t term is -17.55102041t. Take half its coefficient (-8.775510205). Square it (77.00957936) and add it to both sides. Add '77.00957936' to each side of the equation. -17.55102041t + 77.00957936 + t2 = -40.3877551 + 77.00957936 Reorder the terms: 77.00957936 + -17.55102041t + t2 = -40.3877551 + 77.00957936 Combine like terms: -40.3877551 + 77.00957936 = 36.62182426 77.00957936 + -17.55102041t + t2 = 36.62182426 Factor a perfect square on the left side: (t + -8.775510205)(t + -8.775510205) = 36.62182426 Calculate the square root of the right side: 6.051596836 Break this problem into two subproblems by setting (t + -8.775510205) equal to 6.051596836 and -6.051596836.Subproblem 1
t + -8.775510205 = 6.051596836 Simplifying t + -8.775510205 = 6.051596836 Reorder the terms: -8.775510205 + t = 6.051596836 Solving -8.775510205 + t = 6.051596836 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.775510205' to each side of the equation. -8.775510205 + 8.775510205 + t = 6.051596836 + 8.775510205 Combine like terms: -8.775510205 + 8.775510205 = 0.000000000 0.000000000 + t = 6.051596836 + 8.775510205 t = 6.051596836 + 8.775510205 Combine like terms: 6.051596836 + 8.775510205 = 14.827107041 t = 14.827107041 Simplifying t = 14.827107041Subproblem 2
t + -8.775510205 = -6.051596836 Simplifying t + -8.775510205 = -6.051596836 Reorder the terms: -8.775510205 + t = -6.051596836 Solving -8.775510205 + t = -6.051596836 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.775510205' to each side of the equation. -8.775510205 + 8.775510205 + t = -6.051596836 + 8.775510205 Combine like terms: -8.775510205 + 8.775510205 = 0.000000000 0.000000000 + t = -6.051596836 + 8.775510205 t = -6.051596836 + 8.775510205 Combine like terms: -6.051596836 + 8.775510205 = 2.723913369 t = 2.723913369 Simplifying t = 2.723913369Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.827107041, 2.723913369}
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