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Simplifying -2x(x + 1) + 9x = 54 Reorder the terms: -2x(1 + x) + 9x = 54 (1 * -2x + x * -2x) + 9x = 54 (-2x + -2x2) + 9x = 54 Reorder the terms: -2x + 9x + -2x2 = 54 Combine like terms: -2x + 9x = 7x 7x + -2x2 = 54 Solving 7x + -2x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 7x + -2x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 27 + -3.5x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -3.5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -3.5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -3.5x + x2 = 0 + -27 -3.5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -3.5x + x2 = -27 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -27 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -27 + 3.0625 Combine like terms: -27 + 3.0625 = -23.9375 3.0625 + -3.5x + x2 = -23.9375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -23.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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