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Simplifying 4x + -16 = 2x2 + x + -6 Reorder the terms: -16 + 4x = 2x2 + x + -6 Reorder the terms: -16 + 4x = -6 + x + 2x2 Solving -16 + 4x = -6 + x + 2x2 Solving for variable 'x'. Reorder the terms: -16 + 6 + 4x + -1x + -2x2 = -6 + x + 2x2 + 6 + -1x + -2x2 Combine like terms: -16 + 6 = -10 -10 + 4x + -1x + -2x2 = -6 + x + 2x2 + 6 + -1x + -2x2 Combine like terms: 4x + -1x = 3x -10 + 3x + -2x2 = -6 + x + 2x2 + 6 + -1x + -2x2 Reorder the terms: -10 + 3x + -2x2 = -6 + 6 + x + -1x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 -10 + 3x + -2x2 = 0 + x + -1x + 2x2 + -2x2 -10 + 3x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 -10 + 3x + -2x2 = 0 + 2x2 + -2x2 -10 + 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -1.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -1.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1.5x + x2 = 0 + -5 -1.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1.5x + x2 = -5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -5 + 0.5625 Combine like terms: -5 + 0.5625 = -4.4375 0.5625 + -1.5x + x2 = -4.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -4.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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