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Simplifying 0 = 0.5x2 + -1.5x + 1.4 Reorder the terms: 0 = 1.4 + -1.5x + 0.5x2 Solving 0 = 1.4 + -1.5x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -1.4 = -1.4 -1.4 + 1.5x + -0.5x2 = 1.4 + -1.5x + 0.5x2 + -1.4 + 1.5x + -0.5x2 Reorder the terms: -1.4 + 1.5x + -0.5x2 = 1.4 + -1.4 + -1.5x + 1.5x + 0.5x2 + -0.5x2 Combine like terms: 1.4 + -1.4 = 0.0 -1.4 + 1.5x + -0.5x2 = 0.0 + -1.5x + 1.5x + 0.5x2 + -0.5x2 -1.4 + 1.5x + -0.5x2 = -1.5x + 1.5x + 0.5x2 + -0.5x2 Combine like terms: -1.5x + 1.5x = 0.0 -1.4 + 1.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 -1.4 + 1.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -1.4 + 1.5x + -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'. 2.8 + -3x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + -3x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + -3x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + -3x + x2 = 0 + -2.8 -3x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 -3x + x2 = -2.8 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 = -2.8 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.8 + 2.25 Combine like terms: -2.8 + 2.25 = -0.55 2.25 + -3x + x2 = -0.55 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -0.55 Can't calculate square root of the right side. The solution to this equation could not be determined.
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