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Simplifying 85 = 195t + -16t2 Solving 85 = 195t + -16t2 Solving for variable 't'. Reorder the terms: 85 + -195t + 16t2 = 195t + -195t + -16t2 + 16t2 Combine like terms: 195t + -195t = 0 85 + -195t + 16t2 = 0 + -16t2 + 16t2 85 + -195t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 85 + -195t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.3125 + -12.1875t + t2 = 0 Move the constant term to the right: Add '-5.3125' to each side of the equation. 5.3125 + -12.1875t + -5.3125 + t2 = 0 + -5.3125 Reorder the terms: 5.3125 + -5.3125 + -12.1875t + t2 = 0 + -5.3125 Combine like terms: 5.3125 + -5.3125 = 0.0000 0.0000 + -12.1875t + t2 = 0 + -5.3125 -12.1875t + t2 = 0 + -5.3125 Combine like terms: 0 + -5.3125 = -5.3125 -12.1875t + t2 = -5.3125 The t term is -12.1875t. Take half its coefficient (-6.09375). Square it (37.13378906) and add it to both sides. Add '37.13378906' to each side of the equation. -12.1875t + 37.13378906 + t2 = -5.3125 + 37.13378906 Reorder the terms: 37.13378906 + -12.1875t + t2 = -5.3125 + 37.13378906 Combine like terms: -5.3125 + 37.13378906 = 31.82128906 37.13378906 + -12.1875t + t2 = 31.82128906 Factor a perfect square on the left side: (t + -6.09375)(t + -6.09375) = 31.82128906 Calculate the square root of the right side: 5.641036169 Break this problem into two subproblems by setting (t + -6.09375) equal to 5.641036169 and -5.641036169.Subproblem 1
t + -6.09375 = 5.641036169 Simplifying t + -6.09375 = 5.641036169 Reorder the terms: -6.09375 + t = 5.641036169 Solving -6.09375 + t = 5.641036169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.09375' to each side of the equation. -6.09375 + 6.09375 + t = 5.641036169 + 6.09375 Combine like terms: -6.09375 + 6.09375 = 0.00000 0.00000 + t = 5.641036169 + 6.09375 t = 5.641036169 + 6.09375 Combine like terms: 5.641036169 + 6.09375 = 11.734786169 t = 11.734786169 Simplifying t = 11.734786169Subproblem 2
t + -6.09375 = -5.641036169 Simplifying t + -6.09375 = -5.641036169 Reorder the terms: -6.09375 + t = -5.641036169 Solving -6.09375 + t = -5.641036169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.09375' to each side of the equation. -6.09375 + 6.09375 + t = -5.641036169 + 6.09375 Combine like terms: -6.09375 + 6.09375 = 0.00000 0.00000 + t = -5.641036169 + 6.09375 t = -5.641036169 + 6.09375 Combine like terms: -5.641036169 + 6.09375 = 0.452713831 t = 0.452713831 Simplifying t = 0.452713831Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.734786169, 0.452713831}
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