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Simplifying (6t2 + -2t + 3) + (-4t2 + 7t + 5) = 0 Reorder the terms: (3 + -2t + 6t2) + (-4t2 + 7t + 5) = 0 Remove parenthesis around (3 + -2t + 6t2) 3 + -2t + 6t2 + (-4t2 + 7t + 5) = 0 Reorder the terms: 3 + -2t + 6t2 + (5 + 7t + -4t2) = 0 Remove parenthesis around (5 + 7t + -4t2) 3 + -2t + 6t2 + 5 + 7t + -4t2 = 0 Reorder the terms: 3 + 5 + -2t + 7t + 6t2 + -4t2 = 0 Combine like terms: 3 + 5 = 8 8 + -2t + 7t + 6t2 + -4t2 = 0 Combine like terms: -2t + 7t = 5t 8 + 5t + 6t2 + -4t2 = 0 Combine like terms: 6t2 + -4t2 = 2t2 8 + 5t + 2t2 = 0 Solving 8 + 5t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 2.5t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.5t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + 2.5t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.5t + t2 = 0 + -4 2.5t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.5t + t2 = -4 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = -4 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = -4 + 1.5625 Combine like terms: -4 + 1.5625 = -2.4375 1.5625 + 2.5t + t2 = -2.4375 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = -2.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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