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Simplifying 4x2 + -19x + 32 = -6x2 + -6x + -14 Reorder the terms: 32 + -19x + 4x2 = -6x2 + -6x + -14 Reorder the terms: 32 + -19x + 4x2 = -14 + -6x + -6x2 Solving 32 + -19x + 4x2 = -14 + -6x + -6x2 Solving for variable 'x'. Reorder the terms: 32 + 14 + -19x + 6x + 4x2 + 6x2 = -14 + -6x + -6x2 + 14 + 6x + 6x2 Combine like terms: 32 + 14 = 46 46 + -19x + 6x + 4x2 + 6x2 = -14 + -6x + -6x2 + 14 + 6x + 6x2 Combine like terms: -19x + 6x = -13x 46 + -13x + 4x2 + 6x2 = -14 + -6x + -6x2 + 14 + 6x + 6x2 Combine like terms: 4x2 + 6x2 = 10x2 46 + -13x + 10x2 = -14 + -6x + -6x2 + 14 + 6x + 6x2 Reorder the terms: 46 + -13x + 10x2 = -14 + 14 + -6x + 6x + -6x2 + 6x2 Combine like terms: -14 + 14 = 0 46 + -13x + 10x2 = 0 + -6x + 6x + -6x2 + 6x2 46 + -13x + 10x2 = -6x + 6x + -6x2 + 6x2 Combine like terms: -6x + 6x = 0 46 + -13x + 10x2 = 0 + -6x2 + 6x2 46 + -13x + 10x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 46 + -13x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 4.6 + -1.3x + x2 = 0.0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + -1.3x + -4.6 + x2 = 0.0 + -4.6 Reorder the terms: 4.6 + -4.6 + -1.3x + x2 = 0.0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + -1.3x + x2 = 0.0 + -4.6 -1.3x + x2 = 0.0 + -4.6 Combine like terms: 0.0 + -4.6 = -4.6 -1.3x + x2 = -4.6 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = -4.6 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = -4.6 + 0.4225 Combine like terms: -4.6 + 0.4225 = -4.1775 0.4225 + -1.3x + x2 = -4.1775 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = -4.1775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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