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Simplifying (t + -7)(t + -7) = (t + 7)(t + 7) + 168 Reorder the terms: (-7 + t)(t + -7) = (t + 7)(t + 7) + 168 Reorder the terms: (-7 + t)(-7 + t) = (t + 7)(t + 7) + 168 Multiply (-7 + t) * (-7 + t) (-7(-7 + t) + t(-7 + t)) = (t + 7)(t + 7) + 168 ((-7 * -7 + t * -7) + t(-7 + t)) = (t + 7)(t + 7) + 168 ((49 + -7t) + t(-7 + t)) = (t + 7)(t + 7) + 168 (49 + -7t + (-7 * t + t * t)) = (t + 7)(t + 7) + 168 (49 + -7t + (-7t + t2)) = (t + 7)(t + 7) + 168 Combine like terms: -7t + -7t = -14t (49 + -14t + t2) = (t + 7)(t + 7) + 168 Reorder the terms: 49 + -14t + t2 = (7 + t)(t + 7) + 168 Reorder the terms: 49 + -14t + t2 = (7 + t)(7 + t) + 168 Multiply (7 + t) * (7 + t) 49 + -14t + t2 = (7(7 + t) + t(7 + t)) + 168 49 + -14t + t2 = ((7 * 7 + t * 7) + t(7 + t)) + 168 49 + -14t + t2 = ((49 + 7t) + t(7 + t)) + 168 49 + -14t + t2 = (49 + 7t + (7 * t + t * t)) + 168 49 + -14t + t2 = (49 + 7t + (7t + t2)) + 168 Combine like terms: 7t + 7t = 14t 49 + -14t + t2 = (49 + 14t + t2) + 168 Reorder the terms: 49 + -14t + t2 = 49 + 168 + 14t + t2 Combine like terms: 49 + 168 = 217 49 + -14t + t2 = 217 + 14t + t2 Add '-1t2' to each side of the equation. 49 + -14t + t2 + -1t2 = 217 + 14t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 49 + -14t + 0 = 217 + 14t + t2 + -1t2 49 + -14t = 217 + 14t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 49 + -14t = 217 + 14t + 0 49 + -14t = 217 + 14t Solving 49 + -14t = 217 + 14t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14t' to each side of the equation. 49 + -14t + -14t = 217 + 14t + -14t Combine like terms: -14t + -14t = -28t 49 + -28t = 217 + 14t + -14t Combine like terms: 14t + -14t = 0 49 + -28t = 217 + 0 49 + -28t = 217 Add '-49' to each side of the equation. 49 + -49 + -28t = 217 + -49 Combine like terms: 49 + -49 = 0 0 + -28t = 217 + -49 -28t = 217 + -49 Combine like terms: 217 + -49 = 168 -28t = 168 Divide each side by '-28'. t = -6 Simplifying t = -6
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