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Simplifying 0 = 2x2 + -11x + 51 Reorder the terms: 0 = 51 + -11x + 2x2 Solving 0 = 51 + -11x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -51 = -51 -51 + 11x + -2x2 = 51 + -11x + 2x2 + -51 + 11x + -2x2 Reorder the terms: -51 + 11x + -2x2 = 51 + -51 + -11x + 11x + 2x2 + -2x2 Combine like terms: 51 + -51 = 0 -51 + 11x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2 -51 + 11x + -2x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -51 + 11x + -2x2 = 0 + 2x2 + -2x2 -51 + 11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -51 + 11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 25.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + -5.5x + -25.5 + x2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + -5.5x + x2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + -5.5x + x2 = 0 + -25.5 -5.5x + x2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 -5.5x + x2 = -25.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -25.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -25.5 + 7.5625 Combine like terms: -25.5 + 7.5625 = -17.9375 7.5625 + -5.5x + x2 = -17.9375 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = -17.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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