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Simplifying 3x2 + 12 + 2x = x2 + -11 + -5x Reorder the terms: 12 + 2x + 3x2 = x2 + -11 + -5x Reorder the terms: 12 + 2x + 3x2 = -11 + -5x + x2 Solving 12 + 2x + 3x2 = -11 + -5x + x2 Solving for variable 'x'. Reorder the terms: 12 + 11 + 2x + 5x + 3x2 + -1x2 = -11 + -5x + x2 + 11 + 5x + -1x2 Combine like terms: 12 + 11 = 23 23 + 2x + 5x + 3x2 + -1x2 = -11 + -5x + x2 + 11 + 5x + -1x2 Combine like terms: 2x + 5x = 7x 23 + 7x + 3x2 + -1x2 = -11 + -5x + x2 + 11 + 5x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 23 + 7x + 2x2 = -11 + -5x + x2 + 11 + 5x + -1x2 Reorder the terms: 23 + 7x + 2x2 = -11 + 11 + -5x + 5x + x2 + -1x2 Combine like terms: -11 + 11 = 0 23 + 7x + 2x2 = 0 + -5x + 5x + x2 + -1x2 23 + 7x + 2x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 23 + 7x + 2x2 = 0 + x2 + -1x2 23 + 7x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 23 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + 3.5x + -11.5 + x2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + 3.5x + x2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + 3.5x + x2 = 0 + -11.5 3.5x + x2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 3.5x + x2 = -11.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -11.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -11.5 + 3.0625 Combine like terms: -11.5 + 3.0625 = -8.4375 3.0625 + 3.5x + x2 = -8.4375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -8.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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