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Simplifying (t + -1)(t + -1) = (t + 6)(t + -7) + 9 Reorder the terms: (-1 + t)(t + -1) = (t + 6)(t + -7) + 9 Reorder the terms: (-1 + t)(-1 + t) = (t + 6)(t + -7) + 9 Multiply (-1 + t) * (-1 + t) (-1(-1 + t) + t(-1 + t)) = (t + 6)(t + -7) + 9 ((-1 * -1 + t * -1) + t(-1 + t)) = (t + 6)(t + -7) + 9 ((1 + -1t) + t(-1 + t)) = (t + 6)(t + -7) + 9 (1 + -1t + (-1 * t + t * t)) = (t + 6)(t + -7) + 9 (1 + -1t + (-1t + t2)) = (t + 6)(t + -7) + 9 Combine like terms: -1t + -1t = -2t (1 + -2t + t2) = (t + 6)(t + -7) + 9 Reorder the terms: 1 + -2t + t2 = (6 + t)(t + -7) + 9 Reorder the terms: 1 + -2t + t2 = (6 + t)(-7 + t) + 9 Multiply (6 + t) * (-7 + t) 1 + -2t + t2 = (6(-7 + t) + t(-7 + t)) + 9 1 + -2t + t2 = ((-7 * 6 + t * 6) + t(-7 + t)) + 9 1 + -2t + t2 = ((-42 + 6t) + t(-7 + t)) + 9 1 + -2t + t2 = (-42 + 6t + (-7 * t + t * t)) + 9 1 + -2t + t2 = (-42 + 6t + (-7t + t2)) + 9 Combine like terms: 6t + -7t = -1t 1 + -2t + t2 = (-42 + -1t + t2) + 9 Reorder the terms: 1 + -2t + t2 = -42 + 9 + -1t + t2 Combine like terms: -42 + 9 = -33 1 + -2t + t2 = -33 + -1t + t2 Add '-1t2' to each side of the equation. 1 + -2t + t2 + -1t2 = -33 + -1t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 1 + -2t + 0 = -33 + -1t + t2 + -1t2 1 + -2t = -33 + -1t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 1 + -2t = -33 + -1t + 0 1 + -2t = -33 + -1t Solving 1 + -2t = -33 + -1t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add 't' to each side of the equation. 1 + -2t + t = -33 + -1t + t Combine like terms: -2t + t = -1t 1 + -1t = -33 + -1t + t Combine like terms: -1t + t = 0 1 + -1t = -33 + 0 1 + -1t = -33 Add '-1' to each side of the equation. 1 + -1 + -1t = -33 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = -33 + -1 -1t = -33 + -1 Combine like terms: -33 + -1 = -34 -1t = -34 Divide each side by '-1'. t = 34 Simplifying t = 34
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