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Simplifying (3x2 + -2x + 4) + -1(-5x2 + 3x + -8) = 0 Reorder the terms: (4 + -2x + 3x2) + -1(-5x2 + 3x + -8) = 0 Remove parenthesis around (4 + -2x + 3x2) 4 + -2x + 3x2 + -1(-5x2 + 3x + -8) = 0 Reorder the terms: 4 + -2x + 3x2 + -1(-8 + 3x + -5x2) = 0 4 + -2x + 3x2 + (-8 * -1 + 3x * -1 + -5x2 * -1) = 0 4 + -2x + 3x2 + (8 + -3x + 5x2) = 0 Reorder the terms: 4 + 8 + -2x + -3x + 3x2 + 5x2 = 0 Combine like terms: 4 + 8 = 12 12 + -2x + -3x + 3x2 + 5x2 = 0 Combine like terms: -2x + -3x = -5x 12 + -5x + 3x2 + 5x2 = 0 Combine like terms: 3x2 + 5x2 = 8x2 12 + -5x + 8x2 = 0 Solving 12 + -5x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + -0.625x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.625x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.625x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.625x + x2 = 0 + -1.5 -0.625x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.625x + x2 = -1.5 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = -1.5 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = -1.5 + 0.09765625 Combine like terms: -1.5 + 0.09765625 = -1.40234375 0.09765625 + -0.625x + x2 = -1.40234375 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = -1.40234375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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