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Simplifying x2 + 7x + 10 = -27 Reorder the terms: 10 + 7x + x2 = -27 Solving 10 + 7x + x2 = -27 Solving for variable 'x'. Reorder the terms: 10 + 27 + 7x + x2 = -27 + 27 Combine like terms: 10 + 27 = 37 37 + 7x + x2 = -27 + 27 Combine like terms: -27 + 27 = 0 37 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 7x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 7x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 7x + x2 = 0 + -37 7x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 7x + x2 = -37 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -37 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -37 + 12.25 Combine like terms: -37 + 12.25 = -24.75 12.25 + 7x + x2 = -24.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -24.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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