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Simplifying x2 + 3x + 27 = 8x + -3 Reorder the terms: 27 + 3x + x2 = 8x + -3 Reorder the terms: 27 + 3x + x2 = -3 + 8x Solving 27 + 3x + x2 = -3 + 8x Solving for variable 'x'. Reorder the terms: 27 + 3 + 3x + -8x + x2 = -3 + 8x + 3 + -8x Combine like terms: 27 + 3 = 30 30 + 3x + -8x + x2 = -3 + 8x + 3 + -8x Combine like terms: 3x + -8x = -5x 30 + -5x + x2 = -3 + 8x + 3 + -8x Reorder the terms: 30 + -5x + x2 = -3 + 3 + 8x + -8x Combine like terms: -3 + 3 = 0 30 + -5x + x2 = 0 + 8x + -8x 30 + -5x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 30 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -5x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -5x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -5x + x2 = 0 + -30 -5x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -5x + x2 = -30 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -30 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -30 + 6.25 Combine like terms: -30 + 6.25 = -23.75 6.25 + -5x + x2 = -23.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -23.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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