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Simplifying 12x = x2 + 11x + 24 Reorder the terms: 12x = 24 + 11x + x2 Solving 12x = 24 + 11x + x2 Solving for variable 'x'. Reorder the terms: -24 + 12x + -11x + -1x2 = 24 + 11x + x2 + -24 + -11x + -1x2 Combine like terms: 12x + -11x = 1x -24 + 1x + -1x2 = 24 + 11x + x2 + -24 + -11x + -1x2 Reorder the terms: -24 + 1x + -1x2 = 24 + -24 + 11x + -11x + x2 + -1x2 Combine like terms: 24 + -24 = 0 -24 + 1x + -1x2 = 0 + 11x + -11x + x2 + -1x2 -24 + 1x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 -24 + 1x + -1x2 = 0 + x2 + -1x2 -24 + 1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -24 + 1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -1x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -1x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -1x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x + x2 = 0 + -24 -1x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -1x + x2 = -24 The x term is -1x. 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. -1x + 0.25 + x2 = -24 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -24 + 0.25 Combine like terms: -24 + 0.25 = -23.75 0.25 + -1x + x2 = -23.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -23.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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