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Simplifying x(2x + -6) + 5 = (1 + -3x)(x + 1) Reorder the terms: x(-6 + 2x) + 5 = (1 + -3x)(x + 1) (-6 * x + 2x * x) + 5 = (1 + -3x)(x + 1) (-6x + 2x2) + 5 = (1 + -3x)(x + 1) Reorder the terms: 5 + -6x + 2x2 = (1 + -3x)(x + 1) Reorder the terms: 5 + -6x + 2x2 = (1 + -3x)(1 + x) Multiply (1 + -3x) * (1 + x) 5 + -6x + 2x2 = (1(1 + x) + -3x * (1 + x)) 5 + -6x + 2x2 = ((1 * 1 + x * 1) + -3x * (1 + x)) 5 + -6x + 2x2 = ((1 + 1x) + -3x * (1 + x)) 5 + -6x + 2x2 = (1 + 1x + (1 * -3x + x * -3x)) 5 + -6x + 2x2 = (1 + 1x + (-3x + -3x2)) Combine like terms: 1x + -3x = -2x 5 + -6x + 2x2 = (1 + -2x + -3x2) Solving 5 + -6x + 2x2 = 1 + -2x + -3x2 Solving for variable 'x'. Reorder the terms: 5 + -1 + -6x + 2x + 2x2 + 3x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2 Combine like terms: 5 + -1 = 4 4 + -6x + 2x + 2x2 + 3x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2 Combine like terms: -6x + 2x = -4x 4 + -4x + 2x2 + 3x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2 Combine like terms: 2x2 + 3x2 = 5x2 4 + -4x + 5x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2 Reorder the terms: 4 + -4x + 5x2 = 1 + -1 + -2x + 2x + -3x2 + 3x2 Combine like terms: 1 + -1 = 0 4 + -4x + 5x2 = 0 + -2x + 2x + -3x2 + 3x2 4 + -4x + 5x2 = -2x + 2x + -3x2 + 3x2 Combine like terms: -2x + 2x = 0 4 + -4x + 5x2 = 0 + -3x2 + 3x2 4 + -4x + 5x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 4 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -0.8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -0.8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -0.8x + x2 = 0 + -0.8 -0.8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -0.8x + x2 = -0.8 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.8 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.8 + 0.16 Combine like terms: -0.8 + 0.16 = -0.64 0.16 + -0.8x + x2 = -0.64 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = -0.64 Can't calculate square root of the right side. The solution to this equation could not be determined.
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