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Simplifying 3t2 + 8t + 5 = 2t2 Reorder the terms: 5 + 8t + 3t2 = 2t2 Solving 5 + 8t + 3t2 = 2t2 Solving for variable 't'. Combine like terms: 3t2 + -2t2 = 1t2 5 + 8t + 1t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 5 + 8t + 1t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 8t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + 8t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8t + t2 = 0 + -5 8t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 8t + t2 = -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 = -5 + 16 Reorder the terms: 16 + 8t + t2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + 8t + t2 = 11 Factor a perfect square on the left side: (t + 4)(t + 4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (t + 4) equal to 3.31662479 and -3.31662479.Subproblem 1
t + 4 = 3.31662479 Simplifying t + 4 = 3.31662479 Reorder the terms: 4 + t = 3.31662479 Solving 4 + t = 3.31662479 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 = 3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + t = 3.31662479 + -4 t = 3.31662479 + -4 Combine like terms: 3.31662479 + -4 = -0.68337521 t = -0.68337521 Simplifying t = -0.68337521Subproblem 2
t + 4 = -3.31662479 Simplifying t + 4 = -3.31662479 Reorder the terms: 4 + t = -3.31662479 Solving 4 + t = -3.31662479 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 = -3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + t = -3.31662479 + -4 t = -3.31662479 + -4 Combine like terms: -3.31662479 + -4 = -7.31662479 t = -7.31662479 Simplifying t = -7.31662479Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.68337521, -7.31662479}
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