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Simplifying 0 = -0.5x2 + 1.1x + -2.3 Reorder the terms: 0 = -2.3 + 1.1x + -0.5x2 Solving 0 = -2.3 + 1.1x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + 2.3 = 2.3 2.3 + -1.1x + 0.5x2 = -2.3 + 1.1x + -0.5x2 + 2.3 + -1.1x + 0.5x2 Reorder the terms: 2.3 + -1.1x + 0.5x2 = -2.3 + 2.3 + 1.1x + -1.1x + -0.5x2 + 0.5x2 Combine like terms: -2.3 + 2.3 = 0.0 2.3 + -1.1x + 0.5x2 = 0.0 + 1.1x + -1.1x + -0.5x2 + 0.5x2 2.3 + -1.1x + 0.5x2 = 1.1x + -1.1x + -0.5x2 + 0.5x2 Combine like terms: 1.1x + -1.1x = 0.0 2.3 + -1.1x + 0.5x2 = 0.0 + -0.5x2 + 0.5x2 2.3 + -1.1x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 2.3 + -1.1x + 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'. 4.6 + -2.2x + x2 = 0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + -2.2x + -4.6 + x2 = 0 + -4.6 Reorder the terms: 4.6 + -4.6 + -2.2x + x2 = 0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + -2.2x + x2 = 0 + -4.6 -2.2x + x2 = 0 + -4.6 Combine like terms: 0 + -4.6 = -4.6 -2.2x + x2 = -4.6 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -4.6 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -4.6 + 1.21 Combine like terms: -4.6 + 1.21 = -3.39 1.21 + -2.2x + x2 = -3.39 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = -3.39 Can't calculate square root of the right side. The solution to this equation could not be determined.
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