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Simplifying (3x2 + 4x + 3) + (8x2 + 7x) = 0 Reorder the terms: (3 + 4x + 3x2) + (8x2 + 7x) = 0 Remove parenthesis around (3 + 4x + 3x2) 3 + 4x + 3x2 + (8x2 + 7x) = 0 Reorder the terms: 3 + 4x + 3x2 + (7x + 8x2) = 0 Remove parenthesis around (7x + 8x2) 3 + 4x + 3x2 + 7x + 8x2 = 0 Reorder the terms: 3 + 4x + 7x + 3x2 + 8x2 = 0 Combine like terms: 4x + 7x = 11x 3 + 11x + 3x2 + 8x2 = 0 Combine like terms: 3x2 + 8x2 = 11x2 3 + 11x + 11x2 = 0 Solving 3 + 11x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.2727272727 + x + x2 = 0 Move the constant term to the right: Add '-0.2727272727' to each side of the equation. 0.2727272727 + x + -0.2727272727 + x2 = 0 + -0.2727272727 Reorder the terms: 0.2727272727 + -0.2727272727 + x + x2 = 0 + -0.2727272727 Combine like terms: 0.2727272727 + -0.2727272727 = 0.0000000000 0.0000000000 + x + x2 = 0 + -0.2727272727 x + x2 = 0 + -0.2727272727 Combine like terms: 0 + -0.2727272727 = -0.2727272727 x + x2 = -0.2727272727 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.2727272727 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.2727272727 + 0.25 Combine like terms: -0.2727272727 + 0.25 = -0.0227272727 1.25 + x2 = -0.0227272727 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0227272727 Can't calculate square root of the right side. The solution to this equation could not be determined.
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