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Simplifying x2 + 5x = 2 + 3x + -24 Reorder the terms: 5x + x2 = 2 + 3x + -24 Reorder the terms: 5x + x2 = 2 + -24 + 3x Combine like terms: 2 + -24 = -22 5x + x2 = -22 + 3x Solving 5x + x2 = -22 + 3x Solving for variable 'x'. Reorder the terms: 22 + 5x + -3x + x2 = -22 + 3x + 22 + -3x Combine like terms: 5x + -3x = 2x 22 + 2x + x2 = -22 + 3x + 22 + -3x Reorder the terms: 22 + 2x + x2 = -22 + 22 + 3x + -3x Combine like terms: -22 + 22 = 0 22 + 2x + x2 = 0 + 3x + -3x 22 + 2x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 22 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 2x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 2x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 2x + x2 = 0 + -22 2x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 2x + x2 = -22 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -22 + 1 Reorder the terms: 1 + 2x + x2 = -22 + 1 Combine like terms: -22 + 1 = -21 1 + 2x + x2 = -21 Factor a perfect square on the left side: (x + 1)(x + 1) = -21 Can't calculate square root of the right side. The solution to this equation could not be determined.
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