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Simplifying 5(x + 1) = x(3 + -1x) Reorder the terms: 5(1 + x) = x(3 + -1x) (1 * 5 + x * 5) = x(3 + -1x) (5 + 5x) = x(3 + -1x) 5 + 5x = (3 * x + -1x * x) 5 + 5x = (3x + -1x2) Solving 5 + 5x = 3x + -1x2 Solving for variable 'x'. Combine like terms: 5x + -3x = 2x 5 + 2x + x2 = 3x + -1x2 + -3x + x2 Reorder the terms: 5 + 2x + x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 5 + 2x + x2 = 0 + -1x2 + x2 5 + 2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 5 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x + x2 = 0 + -5 2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 2x + x2 = -5 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 = -5 + 1 Reorder the terms: 1 + 2x + x2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + 2x + x2 = -4 Factor a perfect square on the left side: (x + 1)(x + 1) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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