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Simplifying 320 = -16t2 + 80t + 3 Reorder the terms: 320 = 3 + 80t + -16t2 Solving 320 = 3 + 80t + -16t2 Solving for variable 't'. Combine like terms: 320 + -3 = 317 317 + -80t + 16t2 = 3 + 80t + -16t2 + -3 + -80t + 16t2 Reorder the terms: 317 + -80t + 16t2 = 3 + -3 + 80t + -80t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 317 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2 317 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 317 + -80t + 16t2 = 0 + -16t2 + 16t2 317 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 317 + -80t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 19.8125 + -5t + t2 = 0 Move the constant term to the right: Add '-19.8125' to each side of the equation. 19.8125 + -5t + -19.8125 + t2 = 0 + -19.8125 Reorder the terms: 19.8125 + -19.8125 + -5t + t2 = 0 + -19.8125 Combine like terms: 19.8125 + -19.8125 = 0.0000 0.0000 + -5t + t2 = 0 + -19.8125 -5t + t2 = 0 + -19.8125 Combine like terms: 0 + -19.8125 = -19.8125 -5t + t2 = -19.8125 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 = -19.8125 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -19.8125 + 6.25 Combine like terms: -19.8125 + 6.25 = -13.5625 6.25 + -5t + t2 = -13.5625 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = -13.5625 Can't calculate square root of the right side. The solution to this equation could not be determined.
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