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Simplifying 2t2 + -16t + 3 = 0 Reorder the terms: 3 + -16t + 2t2 = 0 Solving 3 + -16t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -8t + t2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -8t + -1.5 + t2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -8t + t2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -8t + t2 = 0 + -1.5 -8t + t2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -8t + t2 = -1.5 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -1.5 + 16 Reorder the terms: 16 + -8t + t2 = -1.5 + 16 Combine like terms: -1.5 + 16 = 14.5 16 + -8t + t2 = 14.5 Factor a perfect square on the left side: (t + -4)(t + -4) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (t + -4) equal to 3.807886553 and -3.807886553.Subproblem 1
t + -4 = 3.807886553 Simplifying t + -4 = 3.807886553 Reorder the terms: -4 + t = 3.807886553 Solving -4 + t = 3.807886553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.807886553 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.807886553 + 4 t = 3.807886553 + 4 Combine like terms: 3.807886553 + 4 = 7.807886553 t = 7.807886553 Simplifying t = 7.807886553Subproblem 2
t + -4 = -3.807886553 Simplifying t + -4 = -3.807886553 Reorder the terms: -4 + t = -3.807886553 Solving -4 + t = -3.807886553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.807886553 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.807886553 + 4 t = -3.807886553 + 4 Combine like terms: -3.807886553 + 4 = 0.192113447 t = 0.192113447 Simplifying t = 0.192113447Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.807886553, 0.192113447}
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