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Simplifying 45 = -16t2 + 45t + 6 Reorder the terms: 45 = 6 + 45t + -16t2 Solving 45 = 6 + 45t + -16t2 Solving for variable 't'. Combine like terms: 45 + -6 = 39 39 + -45t + 16t2 = 6 + 45t + -16t2 + -6 + -45t + 16t2 Reorder the terms: 39 + -45t + 16t2 = 6 + -6 + 45t + -45t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 39 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2 39 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 39 + -45t + 16t2 = 0 + -16t2 + 16t2 39 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 39 + -45t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.4375 + -2.8125t + t2 = 0 Move the constant term to the right: Add '-2.4375' to each side of the equation. 2.4375 + -2.8125t + -2.4375 + t2 = 0 + -2.4375 Reorder the terms: 2.4375 + -2.4375 + -2.8125t + t2 = 0 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + -2.8125t + t2 = 0 + -2.4375 -2.8125t + t2 = 0 + -2.4375 Combine like terms: 0 + -2.4375 = -2.4375 -2.8125t + t2 = -2.4375 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = -2.4375 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = -2.4375 + 1.977539063 Combine like terms: -2.4375 + 1.977539063 = -0.459960937 1.977539063 + -2.8125t + t2 = -0.459960937 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = -0.459960937 Can't calculate square root of the right side. The solution to this equation could not be determined.
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