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Simplifying (3x + 31) + (2x + -6) * x = 0 Reorder the terms: (31 + 3x) + (2x + -6) * x = 0 Remove parenthesis around (31 + 3x) 31 + 3x + (2x + -6) * x = 0 Reorder the terms: 31 + 3x + (-6 + 2x) * x = 0 Reorder the terms for easier multiplication: 31 + 3x + x(-6 + 2x) = 0 31 + 3x + (-6 * x + 2x * x) = 0 31 + 3x + (-6x + 2x2) = 0 Combine like terms: 3x + -6x = -3x 31 + -3x + 2x2 = 0 Solving 31 + -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'. 15.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + -1.5x + -15.5 + x2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + -1.5x + x2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + -1.5x + x2 = 0 + -15.5 -1.5x + x2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 -1.5x + x2 = -15.5 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 = -15.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -15.5 + 0.5625 Combine like terms: -15.5 + 0.5625 = -14.9375 0.5625 + -1.5x + x2 = -14.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -14.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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