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Simplifying 0 = 0.5x2 + 0.5x + 28 Reorder the terms: 0 = 28 + 0.5x + 0.5x2 Solving 0 = 28 + 0.5x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -28 = -28 -28 + -0.5x + -0.5x2 = 28 + 0.5x + 0.5x2 + -28 + -0.5x + -0.5x2 Reorder the terms: -28 + -0.5x + -0.5x2 = 28 + -28 + 0.5x + -0.5x + 0.5x2 + -0.5x2 Combine like terms: 28 + -28 = 0 -28 + -0.5x + -0.5x2 = 0 + 0.5x + -0.5x + 0.5x2 + -0.5x2 -28 + -0.5x + -0.5x2 = 0.5x + -0.5x + 0.5x2 + -0.5x2 Combine like terms: 0.5x + -0.5x = 0.0 -28 + -0.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 -28 + -0.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -28 + -0.5x + -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'. 56 + x + x2 = 0 Move the constant term to the right: Add '-56' to each side of the equation. 56 + x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + x + x2 = 0 + -56 x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 x + x2 = -56 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -56 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -56 + 0.25 Combine like terms: -56 + 0.25 = -55.75 1.25 + x2 = -55.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -55.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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