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Simplifying x2 + 6x + 13 = x + 5 Reorder the terms: 13 + 6x + x2 = x + 5 Reorder the terms: 13 + 6x + x2 = 5 + x Solving 13 + 6x + x2 = 5 + x Solving for variable 'x'. Reorder the terms: 13 + -5 + 6x + -1x + x2 = 5 + x + -5 + -1x Combine like terms: 13 + -5 = 8 8 + 6x + -1x + x2 = 5 + x + -5 + -1x Combine like terms: 6x + -1x = 5x 8 + 5x + x2 = 5 + x + -5 + -1x Reorder the terms: 8 + 5x + x2 = 5 + -5 + x + -1x Combine like terms: 5 + -5 = 0 8 + 5x + x2 = 0 + x + -1x 8 + 5x + x2 = x + -1x Combine like terms: x + -1x = 0 8 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5x + x2 = 0 + -8 5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 5x + x2 = -8 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 = -8 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + 5x + x2 = -1.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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