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Simplifying x = -2x2 + 24x + -100 Reorder the terms: x = -100 + 24x + -2x2 Solving x = -100 + 24x + -2x2 Solving for variable 'x'. Reorder the terms: 100 + x + -24x + 2x2 = -100 + 24x + -2x2 + 100 + -24x + 2x2 Combine like terms: x + -24x = -23x 100 + -23x + 2x2 = -100 + 24x + -2x2 + 100 + -24x + 2x2 Reorder the terms: 100 + -23x + 2x2 = -100 + 100 + 24x + -24x + -2x2 + 2x2 Combine like terms: -100 + 100 = 0 100 + -23x + 2x2 = 0 + 24x + -24x + -2x2 + 2x2 100 + -23x + 2x2 = 24x + -24x + -2x2 + 2x2 Combine like terms: 24x + -24x = 0 100 + -23x + 2x2 = 0 + -2x2 + 2x2 100 + -23x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 100 + -23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 50 + -11.5x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -11.5x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -11.5x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -11.5x + x2 = 0 + -50 -11.5x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -11.5x + x2 = -50 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = -50 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = -50 + 33.0625 Combine like terms: -50 + 33.0625 = -16.9375 33.0625 + -11.5x + x2 = -16.9375 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = -16.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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