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Simplifying -184 = 60t + -4.9t2 Solving -184 = 60t + -4.9t2 Solving for variable 't'. Reorder the terms: -184 + -60t + 4.9t2 = 60t + -60t + -4.9t2 + 4.9t2 Combine like terms: 60t + -60t = 0 -184 + -60t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -184 + -60t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -184 + -60t + 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'. -37.55102041 + -12.24489796t + t2 = 0 Move the constant term to the right: Add '37.55102041' to each side of the equation. -37.55102041 + -12.24489796t + 37.55102041 + t2 = 0 + 37.55102041 Reorder the terms: -37.55102041 + 37.55102041 + -12.24489796t + t2 = 0 + 37.55102041 Combine like terms: -37.55102041 + 37.55102041 = 0.00000000 0.00000000 + -12.24489796t + t2 = 0 + 37.55102041 -12.24489796t + t2 = 0 + 37.55102041 Combine like terms: 0 + 37.55102041 = 37.55102041 -12.24489796t + t2 = 37.55102041 The t term is -12.24489796t. Take half its coefficient (-6.12244898). Square it (37.48438151) and add it to both sides. Add '37.48438151' to each side of the equation. -12.24489796t + 37.48438151 + t2 = 37.55102041 + 37.48438151 Reorder the terms: 37.48438151 + -12.24489796t + t2 = 37.55102041 + 37.48438151 Combine like terms: 37.55102041 + 37.48438151 = 75.03540192 37.48438151 + -12.24489796t + t2 = 75.03540192 Factor a perfect square on the left side: (t + -6.12244898)(t + -6.12244898) = 75.03540192 Calculate the square root of the right side: 8.662297728 Break this problem into two subproblems by setting (t + -6.12244898) equal to 8.662297728 and -8.662297728.Subproblem 1
t + -6.12244898 = 8.662297728 Simplifying t + -6.12244898 = 8.662297728 Reorder the terms: -6.12244898 + t = 8.662297728 Solving -6.12244898 + t = 8.662297728 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.12244898' to each side of the equation. -6.12244898 + 6.12244898 + t = 8.662297728 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + t = 8.662297728 + 6.12244898 t = 8.662297728 + 6.12244898 Combine like terms: 8.662297728 + 6.12244898 = 14.784746708 t = 14.784746708 Simplifying t = 14.784746708Subproblem 2
t + -6.12244898 = -8.662297728 Simplifying t + -6.12244898 = -8.662297728 Reorder the terms: -6.12244898 + t = -8.662297728 Solving -6.12244898 + t = -8.662297728 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.12244898' to each side of the equation. -6.12244898 + 6.12244898 + t = -8.662297728 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + t = -8.662297728 + 6.12244898 t = -8.662297728 + 6.12244898 Combine like terms: -8.662297728 + 6.12244898 = -2.539848748 t = -2.539848748 Simplifying t = -2.539848748Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.784746708, -2.539848748}
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