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Simplifying 3x2 + x + 2.25 = 0 Reorder the terms: 2.25 + x + 3x2 = 0 Solving 2.25 + x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.75 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.3333333333x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.3333333333x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.3333333333x + x2 = 0 + -0.75 0.3333333333x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.3333333333x + x2 = -0.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = -0.75 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + 0.3333333333x + x2 = -0.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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