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Simplifying 2t2 + 3t + 32 = 0 Reorder the terms: 32 + 3t + 2t2 = 0 Solving 32 + 3t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 16 + 1.5t + t2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + 1.5t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + 1.5t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 1.5t + t2 = 0 + -16 1.5t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 1.5t + t2 = -16 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 = -16 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -16 + 0.5625 Combine like terms: -16 + 0.5625 = -15.4375 0.5625 + 1.5t + t2 = -15.4375 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = -15.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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