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Simplifying 0 = 2t2 + -4t + 3 Reorder the terms: 0 = 3 + -4t + 2t2 Solving 0 = 3 + -4t + 2t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + 4t + -2t2 = 3 + -4t + 2t2 + -3 + 4t + -2t2 Reorder the terms: -3 + 4t + -2t2 = 3 + -3 + -4t + 4t + 2t2 + -2t2 Combine like terms: 3 + -3 = 0 -3 + 4t + -2t2 = 0 + -4t + 4t + 2t2 + -2t2 -3 + 4t + -2t2 = -4t + 4t + 2t2 + -2t2 Combine like terms: -4t + 4t = 0 -3 + 4t + -2t2 = 0 + 2t2 + -2t2 -3 + 4t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -3 + 4t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -2t + t2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2t + -1.5 + t2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2t + t2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2t + t2 = 0 + -1.5 -2t + t2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2t + t2 = -1.5 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 = -1.5 + 1 Reorder the terms: 1 + -2t + t2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + -2t + t2 = -0.5 Factor a perfect square on the left side: (t + -1)(t + -1) = -0.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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