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Simplifying 7x2 + x = 12x2 + -3x + 2 Reorder the terms: x + 7x2 = 12x2 + -3x + 2 Reorder the terms: x + 7x2 = 2 + -3x + 12x2 Solving x + 7x2 = 2 + -3x + 12x2 Solving for variable 'x'. Reorder the terms: -2 + x + 3x + 7x2 + -12x2 = 2 + -3x + 12x2 + -2 + 3x + -12x2 Combine like terms: x + 3x = 4x -2 + 4x + 7x2 + -12x2 = 2 + -3x + 12x2 + -2 + 3x + -12x2 Combine like terms: 7x2 + -12x2 = -5x2 -2 + 4x + -5x2 = 2 + -3x + 12x2 + -2 + 3x + -12x2 Reorder the terms: -2 + 4x + -5x2 = 2 + -2 + -3x + 3x + 12x2 + -12x2 Combine like terms: 2 + -2 = 0 -2 + 4x + -5x2 = 0 + -3x + 3x + 12x2 + -12x2 -2 + 4x + -5x2 = -3x + 3x + 12x2 + -12x2 Combine like terms: -3x + 3x = 0 -2 + 4x + -5x2 = 0 + 12x2 + -12x2 -2 + 4x + -5x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -2 + 4x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.4 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.8x + x2 = 0 + -0.4 -0.8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.8x + x2 = -0.4 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 = -0.4 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.4 + 0.16 Combine like terms: -0.4 + 0.16 = -0.24 0.16 + -0.8x + x2 = -0.24 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = -0.24 Can't calculate square root of the right side. The solution to this equation could not be determined.
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