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Simplifying (t + 8)(t) = 12 Reorder the terms: (8 + t)(t) = 12 Reorder the terms for easier multiplication: t(8 + t) = 12 (8 * t + t * t) = 12 (8t + t2) = 12 Solving 8t + t2 = 12 Solving for variable 't'. Reorder the terms: -12 + 8t + t2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 8t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + 8t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 8t + t2 = 0 + 12 8t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 8t + t2 = 12 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 = 12 + 16 Reorder the terms: 16 + 8t + t2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + 8t + t2 = 28 Factor a perfect square on the left side: (t + 4)(t + 4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (t + 4) equal to 5.291502622 and -5.291502622.Subproblem 1
t + 4 = 5.291502622 Simplifying t + 4 = 5.291502622 Reorder the terms: 4 + t = 5.291502622 Solving 4 + t = 5.291502622 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 = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + t = 5.291502622 + -4 t = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 t = 1.291502622 Simplifying t = 1.291502622Subproblem 2
t + 4 = -5.291502622 Simplifying t + 4 = -5.291502622 Reorder the terms: 4 + t = -5.291502622 Solving 4 + t = -5.291502622 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 = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + t = -5.291502622 + -4 t = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 t = -9.291502622 Simplifying t = -9.291502622Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.291502622, -9.291502622}
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