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Simplifying 0 = -16t2 + -32t + -277 Reorder the terms: 0 = -277 + -32t + -16t2 Solving 0 = -277 + -32t + -16t2 Solving for variable 't'. Combine like terms: 0 + 277 = 277 277 + 32t + 16t2 = -277 + -32t + -16t2 + 277 + 32t + 16t2 Reorder the terms: 277 + 32t + 16t2 = -277 + 277 + -32t + 32t + -16t2 + 16t2 Combine like terms: -277 + 277 = 0 277 + 32t + 16t2 = 0 + -32t + 32t + -16t2 + 16t2 277 + 32t + 16t2 = -32t + 32t + -16t2 + 16t2 Combine like terms: -32t + 32t = 0 277 + 32t + 16t2 = 0 + -16t2 + 16t2 277 + 32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 277 + 32t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 17.3125 + 2t + t2 = 0 Move the constant term to the right: Add '-17.3125' to each side of the equation. 17.3125 + 2t + -17.3125 + t2 = 0 + -17.3125 Reorder the terms: 17.3125 + -17.3125 + 2t + t2 = 0 + -17.3125 Combine like terms: 17.3125 + -17.3125 = 0.0000 0.0000 + 2t + t2 = 0 + -17.3125 2t + t2 = 0 + -17.3125 Combine like terms: 0 + -17.3125 = -17.3125 2t + t2 = -17.3125 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = -17.3125 + 1 Reorder the terms: 1 + 2t + t2 = -17.3125 + 1 Combine like terms: -17.3125 + 1 = -16.3125 1 + 2t + t2 = -16.3125 Factor a perfect square on the left side: (t + 1)(t + 1) = -16.3125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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