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Simplifying 127 = -16t2 + 127t Reorder the terms: 127 = 127t + -16t2 Solving 127 = 127t + -16t2 Solving for variable 't'. Reorder the terms: 127 + -127t + 16t2 = 127t + -127t + -16t2 + 16t2 Combine like terms: 127t + -127t = 0 127 + -127t + 16t2 = 0 + -16t2 + 16t2 127 + -127t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 127 + -127t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.9375 + -7.9375t + t2 = 0 Move the constant term to the right: Add '-7.9375' to each side of the equation. 7.9375 + -7.9375t + -7.9375 + t2 = 0 + -7.9375 Reorder the terms: 7.9375 + -7.9375 + -7.9375t + t2 = 0 + -7.9375 Combine like terms: 7.9375 + -7.9375 = 0.0000 0.0000 + -7.9375t + t2 = 0 + -7.9375 -7.9375t + t2 = 0 + -7.9375 Combine like terms: 0 + -7.9375 = -7.9375 -7.9375t + t2 = -7.9375 The t term is -7.9375t. Take half its coefficient (-3.96875). Square it (15.75097656) and add it to both sides. Add '15.75097656' to each side of the equation. -7.9375t + 15.75097656 + t2 = -7.9375 + 15.75097656 Reorder the terms: 15.75097656 + -7.9375t + t2 = -7.9375 + 15.75097656 Combine like terms: -7.9375 + 15.75097656 = 7.81347656 15.75097656 + -7.9375t + t2 = 7.81347656 Factor a perfect square on the left side: (t + -3.96875)(t + -3.96875) = 7.81347656 Calculate the square root of the right side: 2.795259659 Break this problem into two subproblems by setting (t + -3.96875) equal to 2.795259659 and -2.795259659.Subproblem 1
t + -3.96875 = 2.795259659 Simplifying t + -3.96875 = 2.795259659 Reorder the terms: -3.96875 + t = 2.795259659 Solving -3.96875 + t = 2.795259659 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.96875' to each side of the equation. -3.96875 + 3.96875 + t = 2.795259659 + 3.96875 Combine like terms: -3.96875 + 3.96875 = 0.00000 0.00000 + t = 2.795259659 + 3.96875 t = 2.795259659 + 3.96875 Combine like terms: 2.795259659 + 3.96875 = 6.764009659 t = 6.764009659 Simplifying t = 6.764009659Subproblem 2
t + -3.96875 = -2.795259659 Simplifying t + -3.96875 = -2.795259659 Reorder the terms: -3.96875 + t = -2.795259659 Solving -3.96875 + t = -2.795259659 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.96875' to each side of the equation. -3.96875 + 3.96875 + t = -2.795259659 + 3.96875 Combine like terms: -3.96875 + 3.96875 = 0.00000 0.00000 + t = -2.795259659 + 3.96875 t = -2.795259659 + 3.96875 Combine like terms: -2.795259659 + 3.96875 = 1.173490341 t = 1.173490341 Simplifying t = 1.173490341Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.764009659, 1.173490341}
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