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Simplifying 4x2 + 27x + 54 = 0 Reorder the terms: 54 + 27x + 4x2 = 0 Solving 54 + 27x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 13.5 + 6.75x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 6.75x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 6.75x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 6.75x + x2 = 0 + -13.5 6.75x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 6.75x + x2 = -13.5 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = -13.5 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -13.5 + 11.390625 Combine like terms: -13.5 + 11.390625 = -2.109375 11.390625 + 6.75x + x2 = -2.109375 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = -2.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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