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Simplifying 0.5x2 + 3.5x = -12 Reorder the terms: 3.5x + 0.5x2 = -12 Solving 3.5x + 0.5x2 = -12 Solving for variable 'x'. Reorder the terms: 12 + 3.5x + 0.5x2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + 3.5x + 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'. 24 + 7x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + 7x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 7x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 7x + x2 = 0 + -24 7x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 7x + x2 = -24 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -24 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -24 + 12.25 Combine like terms: -24 + 12.25 = -11.75 12.25 + 7x + x2 = -11.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -11.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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