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Simplifying (t + -4)(t + -4) = (t + 4)(t + 4) + 32 Reorder the terms: (-4 + t)(t + -4) = (t + 4)(t + 4) + 32 Reorder the terms: (-4 + t)(-4 + t) = (t + 4)(t + 4) + 32 Multiply (-4 + t) * (-4 + t) (-4(-4 + t) + t(-4 + t)) = (t + 4)(t + 4) + 32 ((-4 * -4 + t * -4) + t(-4 + t)) = (t + 4)(t + 4) + 32 ((16 + -4t) + t(-4 + t)) = (t + 4)(t + 4) + 32 (16 + -4t + (-4 * t + t * t)) = (t + 4)(t + 4) + 32 (16 + -4t + (-4t + t2)) = (t + 4)(t + 4) + 32 Combine like terms: -4t + -4t = -8t (16 + -8t + t2) = (t + 4)(t + 4) + 32 Reorder the terms: 16 + -8t + t2 = (4 + t)(t + 4) + 32 Reorder the terms: 16 + -8t + t2 = (4 + t)(4 + t) + 32 Multiply (4 + t) * (4 + t) 16 + -8t + t2 = (4(4 + t) + t(4 + t)) + 32 16 + -8t + t2 = ((4 * 4 + t * 4) + t(4 + t)) + 32 16 + -8t + t2 = ((16 + 4t) + t(4 + t)) + 32 16 + -8t + t2 = (16 + 4t + (4 * t + t * t)) + 32 16 + -8t + t2 = (16 + 4t + (4t + t2)) + 32 Combine like terms: 4t + 4t = 8t 16 + -8t + t2 = (16 + 8t + t2) + 32 Reorder the terms: 16 + -8t + t2 = 16 + 32 + 8t + t2 Combine like terms: 16 + 32 = 48 16 + -8t + t2 = 48 + 8t + t2 Add '-1t2' to each side of the equation. 16 + -8t + t2 + -1t2 = 48 + 8t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 16 + -8t + 0 = 48 + 8t + t2 + -1t2 16 + -8t = 48 + 8t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 16 + -8t = 48 + 8t + 0 16 + -8t = 48 + 8t Solving 16 + -8t = 48 + 8t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8t' to each side of the equation. 16 + -8t + -8t = 48 + 8t + -8t Combine like terms: -8t + -8t = -16t 16 + -16t = 48 + 8t + -8t Combine like terms: 8t + -8t = 0 16 + -16t = 48 + 0 16 + -16t = 48 Add '-16' to each side of the equation. 16 + -16 + -16t = 48 + -16 Combine like terms: 16 + -16 = 0 0 + -16t = 48 + -16 -16t = 48 + -16 Combine like terms: 48 + -16 = 32 -16t = 32 Divide each side by '-16'. t = -2 Simplifying t = -2
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