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Simplifying 0 = 0.5x2 + -4x + 12 Reorder the terms: 0 = 12 + -4x + 0.5x2 Solving 0 = 12 + -4x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 4x + -0.5x2 = 12 + -4x + 0.5x2 + -12 + 4x + -0.5x2 Reorder the terms: -12 + 4x + -0.5x2 = 12 + -12 + -4x + 4x + 0.5x2 + -0.5x2 Combine like terms: 12 + -12 = 0 -12 + 4x + -0.5x2 = 0 + -4x + 4x + 0.5x2 + -0.5x2 -12 + 4x + -0.5x2 = -4x + 4x + 0.5x2 + -0.5x2 Combine like terms: -4x + 4x = 0 -12 + 4x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -12 + 4x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -12 + 4x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 24 + -8x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -8x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -8x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -8x + x2 = 0 + -24 -8x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -8x + x2 = -24 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -24 + 16 Reorder the terms: 16 + -8x + x2 = -24 + 16 Combine like terms: -24 + 16 = -8 16 + -8x + x2 = -8 Factor a perfect square on the left side: (x + -4)(x + -4) = -8 Can't calculate square root of the right side. The solution to this equation could not be determined.
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