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Simplifying -0.5x2 + 1.5x + 2 = 4 Reorder the terms: 2 + 1.5x + -0.5x2 = 4 Solving 2 + 1.5x + -0.5x2 = 4 Solving for variable 'x'. Reorder the terms: 2 + -4 + 1.5x + -0.5x2 = 4 + -4 Combine like terms: 2 + -4 = -2 -2 + 1.5x + -0.5x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -2 + 1.5x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 4 + -3x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x + x2 = 0 + -4 -3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3x + x2 = -4 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3x + x2 = -1.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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