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Simplifying 68 = 0.8 + 16t + -3.2t2 Solving 68 = 0.8 + 16t + -3.2t2 Solving for variable 't'. Combine like terms: 68 + -0.8 = 67.2 67.2 + -16t + 3.2t2 = 0.8 + 16t + -3.2t2 + -0.8 + -16t + 3.2t2 Reorder the terms: 67.2 + -16t + 3.2t2 = 0.8 + -0.8 + 16t + -16t + -3.2t2 + 3.2t2 Combine like terms: 0.8 + -0.8 = 0.0 67.2 + -16t + 3.2t2 = 0.0 + 16t + -16t + -3.2t2 + 3.2t2 67.2 + -16t + 3.2t2 = 16t + -16t + -3.2t2 + 3.2t2 Combine like terms: 16t + -16t = 0 67.2 + -16t + 3.2t2 = 0 + -3.2t2 + 3.2t2 67.2 + -16t + 3.2t2 = -3.2t2 + 3.2t2 Combine like terms: -3.2t2 + 3.2t2 = 0.0 67.2 + -16t + 3.2t2 = 0.0 Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. 21 + -5t + t2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + -5t + -21 + t2 = 0 + -21 Reorder the terms: 21 + -21 + -5t + t2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -5t + t2 = 0 + -21 -5t + t2 = 0 + -21 Combine like terms: 0 + -21 = -21 -5t + t2 = -21 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -21 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -21 + 6.25 Combine like terms: -21 + 6.25 = -14.75 6.25 + -5t + t2 = -14.75 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = -14.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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