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Simplifying x(x + 3) + x(x + -6) + 35 = 0 Reorder the terms: x(3 + x) + x(x + -6) + 35 = 0 (3 * x + x * x) + x(x + -6) + 35 = 0 (3x + x2) + x(x + -6) + 35 = 0 Reorder the terms: 3x + x2 + x(-6 + x) + 35 = 0 3x + x2 + (-6 * x + x * x) + 35 = 0 3x + x2 + (-6x + x2) + 35 = 0 Reorder the terms: 35 + 3x + -6x + x2 + x2 = 0 Combine like terms: 3x + -6x = -3x 35 + -3x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 35 + -3x + 2x2 = 0 Solving 35 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + -1.5x + -17.5 + x2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + -1.5x + x2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + -1.5x + x2 = 0 + -17.5 -1.5x + x2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 -1.5x + x2 = -17.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -17.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -17.5 + 0.5625 Combine like terms: -17.5 + 0.5625 = -16.9375 0.5625 + -1.5x + x2 = -16.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -16.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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