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Simplifying 4x2 + -9x + -31 = -42 Reorder the terms: -31 + -9x + 4x2 = -42 Solving -31 + -9x + 4x2 = -42 Solving for variable 'x'. Reorder the terms: -31 + 42 + -9x + 4x2 = -42 + 42 Combine like terms: -31 + 42 = 11 11 + -9x + 4x2 = -42 + 42 Combine like terms: -42 + 42 = 0 11 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + -2.25x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -2.25x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -2.25x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -2.25x + x2 = 0 + -2.75 -2.25x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -2.25x + x2 = -2.75 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -2.75 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -2.75 + 1.265625 Combine like terms: -2.75 + 1.265625 = -1.484375 1.265625 + -2.25x + x2 = -1.484375 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = -1.484375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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