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Simplifying x2 + 6x + 11 = 0.5x + 3 Reorder the terms: 11 + 6x + x2 = 0.5x + 3 Reorder the terms: 11 + 6x + x2 = 3 + 0.5x Solving 11 + 6x + x2 = 3 + 0.5x Solving for variable 'x'. Reorder the terms: 11 + -3 + 6x + -0.5x + x2 = 3 + 0.5x + -3 + -0.5x Combine like terms: 11 + -3 = 8 8 + 6x + -0.5x + x2 = 3 + 0.5x + -3 + -0.5x Combine like terms: 6x + -0.5x = 5.5x 8 + 5.5x + x2 = 3 + 0.5x + -3 + -0.5x Reorder the terms: 8 + 5.5x + x2 = 3 + -3 + 0.5x + -0.5x Combine like terms: 3 + -3 = 0 8 + 5.5x + x2 = 0 + 0.5x + -0.5x 8 + 5.5x + x2 = 0.5x + -0.5x Combine like terms: 0.5x + -0.5x = 0.0 8 + 5.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 5.5x + -8 + x2 = 0.0 + -8 Reorder the terms: 8 + -8 + 5.5x + x2 = 0.0 + -8 Combine like terms: 8 + -8 = 0 0 + 5.5x + x2 = 0.0 + -8 5.5x + x2 = 0.0 + -8 Combine like terms: 0.0 + -8 = -8 5.5x + x2 = -8 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -8 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -8 + 7.5625 Combine like terms: -8 + 7.5625 = -0.4375 7.5625 + 5.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = -0.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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