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Simplifying 4x2 + 5x + 54 = 0 Reorder the terms: 54 + 5x + 4x2 = 0 Solving 54 + 5x + 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 + 1.25x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 1.25x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 1.25x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 1.25x + x2 = 0 + -13.5 1.25x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 1.25x + x2 = -13.5 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -13.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -13.5 + 0.390625 Combine like terms: -13.5 + 0.390625 = -13.109375 0.390625 + 1.25x + x2 = -13.109375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -13.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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