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Simplifying 85 = 125t + -16t2 Solving 85 = 125t + -16t2 Solving for variable 't'. Reorder the terms: 85 + -125t + 16t2 = 125t + -125t + -16t2 + 16t2 Combine like terms: 125t + -125t = 0 85 + -125t + 16t2 = 0 + -16t2 + 16t2 85 + -125t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 85 + -125t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.3125 + -7.8125t + t2 = 0 Move the constant term to the right: Add '-5.3125' to each side of the equation. 5.3125 + -7.8125t + -5.3125 + t2 = 0 + -5.3125 Reorder the terms: 5.3125 + -5.3125 + -7.8125t + t2 = 0 + -5.3125 Combine like terms: 5.3125 + -5.3125 = 0.0000 0.0000 + -7.8125t + t2 = 0 + -5.3125 -7.8125t + t2 = 0 + -5.3125 Combine like terms: 0 + -5.3125 = -5.3125 -7.8125t + t2 = -5.3125 The t term is -7.8125t. Take half its coefficient (-3.90625). Square it (15.25878906) and add it to both sides. Add '15.25878906' to each side of the equation. -7.8125t + 15.25878906 + t2 = -5.3125 + 15.25878906 Reorder the terms: 15.25878906 + -7.8125t + t2 = -5.3125 + 15.25878906 Combine like terms: -5.3125 + 15.25878906 = 9.94628906 15.25878906 + -7.8125t + t2 = 9.94628906 Factor a perfect square on the left side: (t + -3.90625)(t + -3.90625) = 9.94628906 Calculate the square root of the right side: 3.153773781 Break this problem into two subproblems by setting (t + -3.90625) equal to 3.153773781 and -3.153773781.Subproblem 1
t + -3.90625 = 3.153773781 Simplifying t + -3.90625 = 3.153773781 Reorder the terms: -3.90625 + t = 3.153773781 Solving -3.90625 + t = 3.153773781 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = 3.153773781 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = 3.153773781 + 3.90625 t = 3.153773781 + 3.90625 Combine like terms: 3.153773781 + 3.90625 = 7.060023781 t = 7.060023781 Simplifying t = 7.060023781Subproblem 2
t + -3.90625 = -3.153773781 Simplifying t + -3.90625 = -3.153773781 Reorder the terms: -3.90625 + t = -3.153773781 Solving -3.90625 + t = -3.153773781 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = -3.153773781 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = -3.153773781 + 3.90625 t = -3.153773781 + 3.90625 Combine like terms: -3.153773781 + 3.90625 = 0.752476219 t = 0.752476219 Simplifying t = 0.752476219Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.060023781, 0.752476219}
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