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Simplifying 0 = 4t2 + -19t + 27 Reorder the terms: 0 = 27 + -19t + 4t2 Solving 0 = 27 + -19t + 4t2 Solving for variable 't'. Combine like terms: 0 + -27 = -27 -27 + 19t + -4t2 = 27 + -19t + 4t2 + -27 + 19t + -4t2 Reorder the terms: -27 + 19t + -4t2 = 27 + -27 + -19t + 19t + 4t2 + -4t2 Combine like terms: 27 + -27 = 0 -27 + 19t + -4t2 = 0 + -19t + 19t + 4t2 + -4t2 -27 + 19t + -4t2 = -19t + 19t + 4t2 + -4t2 Combine like terms: -19t + 19t = 0 -27 + 19t + -4t2 = 0 + 4t2 + -4t2 -27 + 19t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -27 + 19t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 6.75 + -4.75t + t2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -4.75t + -6.75 + t2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -4.75t + t2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -4.75t + t2 = 0 + -6.75 -4.75t + t2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -4.75t + t2 = -6.75 The t term is -4.75t. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75t + 5.640625 + t2 = -6.75 + 5.640625 Reorder the terms: 5.640625 + -4.75t + t2 = -6.75 + 5.640625 Combine like terms: -6.75 + 5.640625 = -1.109375 5.640625 + -4.75t + t2 = -1.109375 Factor a perfect square on the left side: (t + -2.375)(t + -2.375) = -1.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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