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Simplifying 16t2 + -165t + 87 = 0 Reorder the terms: 87 + -165t + 16t2 = 0 Solving 87 + -165t + 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'. 5.4375 + -10.3125t + t2 = 0 Move the constant term to the right: Add '-5.4375' to each side of the equation. 5.4375 + -10.3125t + -5.4375 + t2 = 0 + -5.4375 Reorder the terms: 5.4375 + -5.4375 + -10.3125t + t2 = 0 + -5.4375 Combine like terms: 5.4375 + -5.4375 = 0.0000 0.0000 + -10.3125t + t2 = 0 + -5.4375 -10.3125t + t2 = 0 + -5.4375 Combine like terms: 0 + -5.4375 = -5.4375 -10.3125t + t2 = -5.4375 The t term is -10.3125t. Take half its coefficient (-5.15625). Square it (26.58691406) and add it to both sides. Add '26.58691406' to each side of the equation. -10.3125t + 26.58691406 + t2 = -5.4375 + 26.58691406 Reorder the terms: 26.58691406 + -10.3125t + t2 = -5.4375 + 26.58691406 Combine like terms: -5.4375 + 26.58691406 = 21.14941406 26.58691406 + -10.3125t + t2 = 21.14941406 Factor a perfect square on the left side: (t + -5.15625)(t + -5.15625) = 21.14941406 Calculate the square root of the right side: 4.59884921 Break this problem into two subproblems by setting (t + -5.15625) equal to 4.59884921 and -4.59884921.Subproblem 1
t + -5.15625 = 4.59884921 Simplifying t + -5.15625 = 4.59884921 Reorder the terms: -5.15625 + t = 4.59884921 Solving -5.15625 + t = 4.59884921 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.15625' to each side of the equation. -5.15625 + 5.15625 + t = 4.59884921 + 5.15625 Combine like terms: -5.15625 + 5.15625 = 0.00000 0.00000 + t = 4.59884921 + 5.15625 t = 4.59884921 + 5.15625 Combine like terms: 4.59884921 + 5.15625 = 9.75509921 t = 9.75509921 Simplifying t = 9.75509921Subproblem 2
t + -5.15625 = -4.59884921 Simplifying t + -5.15625 = -4.59884921 Reorder the terms: -5.15625 + t = -4.59884921 Solving -5.15625 + t = -4.59884921 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.15625' to each side of the equation. -5.15625 + 5.15625 + t = -4.59884921 + 5.15625 Combine like terms: -5.15625 + 5.15625 = 0.00000 0.00000 + t = -4.59884921 + 5.15625 t = -4.59884921 + 5.15625 Combine like terms: -4.59884921 + 5.15625 = 0.55740079 t = 0.55740079 Simplifying t = 0.55740079Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.75509921, 0.55740079}
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