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Simplifying 16t2 + -139t + 264 = 0 Reorder the terms: 264 + -139t + 16t2 = 0 Solving 264 + -139t + 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'. 16.5 + -8.6875t + t2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + -8.6875t + -16.5 + t2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + -8.6875t + t2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + -8.6875t + t2 = 0 + -16.5 -8.6875t + t2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 -8.6875t + t2 = -16.5 The t term is -8.6875t. Take half its coefficient (-4.34375). Square it (18.86816406) and add it to both sides. Add '18.86816406' to each side of the equation. -8.6875t + 18.86816406 + t2 = -16.5 + 18.86816406 Reorder the terms: 18.86816406 + -8.6875t + t2 = -16.5 + 18.86816406 Combine like terms: -16.5 + 18.86816406 = 2.36816406 18.86816406 + -8.6875t + t2 = 2.36816406 Factor a perfect square on the left side: (t + -4.34375)(t + -4.34375) = 2.36816406 Calculate the square root of the right side: 1.538884031 Break this problem into two subproblems by setting (t + -4.34375) equal to 1.538884031 and -1.538884031.Subproblem 1
t + -4.34375 = 1.538884031 Simplifying t + -4.34375 = 1.538884031 Reorder the terms: -4.34375 + t = 1.538884031 Solving -4.34375 + t = 1.538884031 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.34375' to each side of the equation. -4.34375 + 4.34375 + t = 1.538884031 + 4.34375 Combine like terms: -4.34375 + 4.34375 = 0.00000 0.00000 + t = 1.538884031 + 4.34375 t = 1.538884031 + 4.34375 Combine like terms: 1.538884031 + 4.34375 = 5.882634031 t = 5.882634031 Simplifying t = 5.882634031Subproblem 2
t + -4.34375 = -1.538884031 Simplifying t + -4.34375 = -1.538884031 Reorder the terms: -4.34375 + t = -1.538884031 Solving -4.34375 + t = -1.538884031 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.34375' to each side of the equation. -4.34375 + 4.34375 + t = -1.538884031 + 4.34375 Combine like terms: -4.34375 + 4.34375 = 0.00000 0.00000 + t = -1.538884031 + 4.34375 t = -1.538884031 + 4.34375 Combine like terms: -1.538884031 + 4.34375 = 2.804865969 t = 2.804865969 Simplifying t = 2.804865969Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.882634031, 2.804865969}
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