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Simplifying 0 = -16t2 + 40t + -27 Reorder the terms: 0 = -27 + 40t + -16t2 Solving 0 = -27 + 40t + -16t2 Solving for variable 't'. Combine like terms: 0 + 27 = 27 27 + -40t + 16t2 = -27 + 40t + -16t2 + 27 + -40t + 16t2 Reorder the terms: 27 + -40t + 16t2 = -27 + 27 + 40t + -40t + -16t2 + 16t2 Combine like terms: -27 + 27 = 0 27 + -40t + 16t2 = 0 + 40t + -40t + -16t2 + 16t2 27 + -40t + 16t2 = 40t + -40t + -16t2 + 16t2 Combine like terms: 40t + -40t = 0 27 + -40t + 16t2 = 0 + -16t2 + 16t2 27 + -40t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 27 + -40t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.6875 + -2.5t + t2 = 0 Move the constant term to the right: Add '-1.6875' to each side of the equation. 1.6875 + -2.5t + -1.6875 + t2 = 0 + -1.6875 Reorder the terms: 1.6875 + -1.6875 + -2.5t + t2 = 0 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + -2.5t + t2 = 0 + -1.6875 -2.5t + t2 = 0 + -1.6875 Combine like terms: 0 + -1.6875 = -1.6875 -2.5t + t2 = -1.6875 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = -1.6875 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = -1.6875 + 1.5625 Combine like terms: -1.6875 + 1.5625 = -0.125 1.5625 + -2.5t + t2 = -0.125 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = -0.125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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