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Simplifying 2t2 = 3t + -5 Reorder the terms: 2t2 = -5 + 3t Solving 2t2 = -5 + 3t Solving for variable 't'. Reorder the terms: 5 + -3t + 2t2 = -5 + 3t + 5 + -3t Reorder the terms: 5 + -3t + 2t2 = -5 + 5 + 3t + -3t Combine like terms: -5 + 5 = 0 5 + -3t + 2t2 = 0 + 3t + -3t 5 + -3t + 2t2 = 3t + -3t Combine like terms: 3t + -3t = 0 5 + -3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -1.5t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1.5t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1.5t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1.5t + t2 = 0 + -2.5 -1.5t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1.5t + t2 = -2.5 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + -1.5t + t2 = -1.9375 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = -1.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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