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Simplifying 23x2 + 69x + 117 = 0 Reorder the terms: 117 + 69x + 23x2 = 0 Solving 117 + 69x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. 5.086956522 + 3x + x2 = 0 Move the constant term to the right: Add '-5.086956522' to each side of the equation. 5.086956522 + 3x + -5.086956522 + x2 = 0 + -5.086956522 Reorder the terms: 5.086956522 + -5.086956522 + 3x + x2 = 0 + -5.086956522 Combine like terms: 5.086956522 + -5.086956522 = 0.000000000 0.000000000 + 3x + x2 = 0 + -5.086956522 3x + x2 = 0 + -5.086956522 Combine like terms: 0 + -5.086956522 = -5.086956522 3x + x2 = -5.086956522 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 = -5.086956522 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -5.086956522 + 2.25 Combine like terms: -5.086956522 + 2.25 = -2.836956522 2.25 + 3x + x2 = -2.836956522 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -2.836956522 Can't calculate square root of the right side. The solution to this equation could not be determined.
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