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Simplifying 35 = -16t2 + 42t + 6 Reorder the terms: 35 = 6 + 42t + -16t2 Solving 35 = 6 + 42t + -16t2 Solving for variable 't'. Combine like terms: 35 + -6 = 29 29 + -42t + 16t2 = 6 + 42t + -16t2 + -6 + -42t + 16t2 Reorder the terms: 29 + -42t + 16t2 = 6 + -6 + 42t + -42t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 29 + -42t + 16t2 = 0 + 42t + -42t + -16t2 + 16t2 29 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 29 + -42t + 16t2 = 0 + -16t2 + 16t2 29 + -42t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 29 + -42t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.8125 + -2.625t + t2 = 0 Move the constant term to the right: Add '-1.8125' to each side of the equation. 1.8125 + -2.625t + -1.8125 + t2 = 0 + -1.8125 Reorder the terms: 1.8125 + -1.8125 + -2.625t + t2 = 0 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + -2.625t + t2 = 0 + -1.8125 -2.625t + t2 = 0 + -1.8125 Combine like terms: 0 + -1.8125 = -1.8125 -2.625t + t2 = -1.8125 The t term is -2.625t. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625t + 1.72265625 + t2 = -1.8125 + 1.72265625 Reorder the terms: 1.72265625 + -2.625t + t2 = -1.8125 + 1.72265625 Combine like terms: -1.8125 + 1.72265625 = -0.08984375 1.72265625 + -2.625t + t2 = -0.08984375 Factor a perfect square on the left side: (t + -1.3125)(t + -1.3125) = -0.08984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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