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Simplifying 1.4t2 + 6.4t + 6.0 = 1.2t + -6.7t2 + -54 Reorder the terms: 6.0 + 6.4t + 1.4t2 = 1.2t + -6.7t2 + -54 Reorder the terms: 6.0 + 6.4t + 1.4t2 = -54 + 1.2t + -6.7t2 Solving 6.0 + 6.4t + 1.4t2 = -54 + 1.2t + -6.7t2 Solving for variable 't'. Reorder the terms: 6.0 + 54 + 6.4t + -1.2t + 1.4t2 + 6.7t2 = -54 + 1.2t + -6.7t2 + 54 + -1.2t + 6.7t2 Combine like terms: 6.0 + 54 = 60 60 + 6.4t + -1.2t + 1.4t2 + 6.7t2 = -54 + 1.2t + -6.7t2 + 54 + -1.2t + 6.7t2 Combine like terms: 6.4t + -1.2t = 5.2t 60 + 5.2t + 1.4t2 + 6.7t2 = -54 + 1.2t + -6.7t2 + 54 + -1.2t + 6.7t2 Combine like terms: 1.4t2 + 6.7t2 = 8.1t2 60 + 5.2t + 8.1t2 = -54 + 1.2t + -6.7t2 + 54 + -1.2t + 6.7t2 Reorder the terms: 60 + 5.2t + 8.1t2 = -54 + 54 + 1.2t + -1.2t + -6.7t2 + 6.7t2 Combine like terms: -54 + 54 = 0 60 + 5.2t + 8.1t2 = 0 + 1.2t + -1.2t + -6.7t2 + 6.7t2 60 + 5.2t + 8.1t2 = 1.2t + -1.2t + -6.7t2 + 6.7t2 Combine like terms: 1.2t + -1.2t = 0.0 60 + 5.2t + 8.1t2 = 0.0 + -6.7t2 + 6.7t2 60 + 5.2t + 8.1t2 = -6.7t2 + 6.7t2 Combine like terms: -6.7t2 + 6.7t2 = 0.0 60 + 5.2t + 8.1t2 = 0.0 Begin completing the square. Divide all terms by 8.1 the coefficient of the squared term: Divide each side by '8.1'. 7.407407407 + 0.6419753086t + t2 = 0 Move the constant term to the right: Add '-7.407407407' to each side of the equation. 7.407407407 + 0.6419753086t + -7.407407407 + t2 = 0 + -7.407407407 Reorder the terms: 7.407407407 + -7.407407407 + 0.6419753086t + t2 = 0 + -7.407407407 Combine like terms: 7.407407407 + -7.407407407 = 0.000000000 0.000000000 + 0.6419753086t + t2 = 0 + -7.407407407 0.6419753086t + t2 = 0 + -7.407407407 Combine like terms: 0 + -7.407407407 = -7.407407407 0.6419753086t + t2 = -7.407407407 The t term is 0.6419753086t. Take half its coefficient (0.3209876543). Square it (0.1030330742) and add it to both sides. Add '0.1030330742' to each side of the equation. 0.6419753086t + 0.1030330742 + t2 = -7.407407407 + 0.1030330742 Reorder the terms: 0.1030330742 + 0.6419753086t + t2 = -7.407407407 + 0.1030330742 Combine like terms: -7.407407407 + 0.1030330742 = -7.3043743328 0.1030330742 + 0.6419753086t + t2 = -7.3043743328 Factor a perfect square on the left side: (t + 0.3209876543)(t + 0.3209876543) = -7.3043743328 Can't calculate square root of the right side. The solution to this equation could not be determined.
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