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Simplifying (3t + 2) + (9t2 + 9t + 3) = 0 Reorder the terms: (2 + 3t) + (9t2 + 9t + 3) = 0 Remove parenthesis around (2 + 3t) 2 + 3t + (9t2 + 9t + 3) = 0 Reorder the terms: 2 + 3t + (3 + 9t + 9t2) = 0 Remove parenthesis around (3 + 9t + 9t2) 2 + 3t + 3 + 9t + 9t2 = 0 Reorder the terms: 2 + 3 + 3t + 9t + 9t2 = 0 Combine like terms: 2 + 3 = 5 5 + 3t + 9t + 9t2 = 0 Combine like terms: 3t + 9t = 12t 5 + 12t + 9t2 = 0 Solving 5 + 12t + 9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + 1.333333333t + t2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + 1.333333333t + -0.5555555556 + t2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + 1.333333333t + t2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + 1.333333333t + t2 = 0 + -0.5555555556 1.333333333t + t2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 1.333333333t + t2 = -0.5555555556 The t term is 1.333333333t. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333t + 0.4444444442 + t2 = -0.5555555556 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333t + t2 = -0.5555555556 + 0.4444444442 Combine like terms: -0.5555555556 + 0.4444444442 = -0.1111111114 0.4444444442 + 1.333333333t + t2 = -0.1111111114 Factor a perfect square on the left side: (t + 0.6666666665)(t + 0.6666666665) = -0.1111111114 Can't calculate square root of the right side. The solution to this equation could not be determined.
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