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Simplifying 2.2 = 16t2 + 12t + 7.8 Reorder the terms: 2.2 = 7.8 + 12t + 16t2 Solving 2.2 = 7.8 + 12t + 16t2 Solving for variable 't'. Combine like terms: 2.2 + -7.8 = -5.6 -5.6 + -12t + -16t2 = 7.8 + 12t + 16t2 + -7.8 + -12t + -16t2 Reorder the terms: -5.6 + -12t + -16t2 = 7.8 + -7.8 + 12t + -12t + 16t2 + -16t2 Combine like terms: 7.8 + -7.8 = 0.0 -5.6 + -12t + -16t2 = 0.0 + 12t + -12t + 16t2 + -16t2 -5.6 + -12t + -16t2 = 12t + -12t + 16t2 + -16t2 Combine like terms: 12t + -12t = 0 -5.6 + -12t + -16t2 = 0 + 16t2 + -16t2 -5.6 + -12t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -5.6 + -12t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.35 + 0.75t + t2 = 0 Move the constant term to the right: Add '-0.35' to each side of the equation. 0.35 + 0.75t + -0.35 + t2 = 0 + -0.35 Reorder the terms: 0.35 + -0.35 + 0.75t + t2 = 0 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + 0.75t + t2 = 0 + -0.35 0.75t + t2 = 0 + -0.35 Combine like terms: 0 + -0.35 = -0.35 0.75t + t2 = -0.35 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = -0.35 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = -0.35 + 0.140625 Combine like terms: -0.35 + 0.140625 = -0.209375 0.140625 + 0.75t + t2 = -0.209375 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = -0.209375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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