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Simplifying 4x2 + 3x + 27 = 0 Reorder the terms: 27 + 3x + 4x2 = 0 Solving 27 + 3x + 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'. 6.75 + 0.75x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + 0.75x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + 0.75x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + 0.75x + x2 = 0 + -6.75 0.75x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 0.75x + x2 = -6.75 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -6.75 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -6.75 + 0.140625 Combine like terms: -6.75 + 0.140625 = -6.609375 0.140625 + 0.75x + x2 = -6.609375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -6.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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