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Simplifying x2 + 4x + 32 = 8x + 5 Reorder the terms: 32 + 4x + x2 = 8x + 5 Reorder the terms: 32 + 4x + x2 = 5 + 8x Solving 32 + 4x + x2 = 5 + 8x Solving for variable 'x'. Reorder the terms: 32 + -5 + 4x + -8x + x2 = 5 + 8x + -5 + -8x Combine like terms: 32 + -5 = 27 27 + 4x + -8x + x2 = 5 + 8x + -5 + -8x Combine like terms: 4x + -8x = -4x 27 + -4x + x2 = 5 + 8x + -5 + -8x Reorder the terms: 27 + -4x + x2 = 5 + -5 + 8x + -8x Combine like terms: 5 + -5 = 0 27 + -4x + x2 = 0 + 8x + -8x 27 + -4x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 27 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -4x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -4x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -4x + x2 = 0 + -27 -4x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -4x + x2 = -27 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -27 + 4 Reorder the terms: 4 + -4x + x2 = -27 + 4 Combine like terms: -27 + 4 = -23 4 + -4x + x2 = -23 Factor a perfect square on the left side: (x + -2)(x + -2) = -23 Can't calculate square root of the right side. The solution to this equation could not be determined.
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