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Simplifying 16t2 + -125t + -144 = 0 Reorder the terms: -144 + -125t + 16t2 = 0 Solving -144 + -125t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9 + -7.8125t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -7.8125t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -7.8125t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7.8125t + t2 = 0 + 9 -7.8125t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -7.8125t + t2 = 9 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 = 9 + 15.25878906 Reorder the terms: 15.25878906 + -7.8125t + t2 = 9 + 15.25878906 Combine like terms: 9 + 15.25878906 = 24.25878906 15.25878906 + -7.8125t + t2 = 24.25878906 Factor a perfect square on the left side: (t + -3.90625)(t + -3.90625) = 24.25878906 Calculate the square root of the right side: 4.925321214 Break this problem into two subproblems by setting (t + -3.90625) equal to 4.925321214 and -4.925321214.Subproblem 1
t + -3.90625 = 4.925321214 Simplifying t + -3.90625 = 4.925321214 Reorder the terms: -3.90625 + t = 4.925321214 Solving -3.90625 + t = 4.925321214 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 = 4.925321214 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = 4.925321214 + 3.90625 t = 4.925321214 + 3.90625 Combine like terms: 4.925321214 + 3.90625 = 8.831571214 t = 8.831571214 Simplifying t = 8.831571214Subproblem 2
t + -3.90625 = -4.925321214 Simplifying t + -3.90625 = -4.925321214 Reorder the terms: -3.90625 + t = -4.925321214 Solving -3.90625 + t = -4.925321214 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 = -4.925321214 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = -4.925321214 + 3.90625 t = -4.925321214 + 3.90625 Combine like terms: -4.925321214 + 3.90625 = -1.019071214 t = -1.019071214 Simplifying t = -1.019071214Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.831571214, -1.019071214}
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