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Simplifying (x) = 3x2 + -5x + 11 x = 3x2 + -5x + 11 Reorder the terms: x = 11 + -5x + 3x2 Solving x = 11 + -5x + 3x2 Solving for variable 'x'. Reorder the terms: -11 + x + 5x + -3x2 = 11 + -5x + 3x2 + -11 + 5x + -3x2 Combine like terms: x + 5x = 6x -11 + 6x + -3x2 = 11 + -5x + 3x2 + -11 + 5x + -3x2 Reorder the terms: -11 + 6x + -3x2 = 11 + -11 + -5x + 5x + 3x2 + -3x2 Combine like terms: 11 + -11 = 0 -11 + 6x + -3x2 = 0 + -5x + 5x + 3x2 + -3x2 -11 + 6x + -3x2 = -5x + 5x + 3x2 + -3x2 Combine like terms: -5x + 5x = 0 -11 + 6x + -3x2 = 0 + 3x2 + -3x2 -11 + 6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -11 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 3.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + -2x + -3.666666667 + x2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + -2x + x2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + -3.666666667 -2x + x2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 -2x + x2 = -3.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -3.666666667 + 1 Reorder the terms: 1 + -2x + x2 = -3.666666667 + 1 Combine like terms: -3.666666667 + 1 = -2.666666667 1 + -2x + x2 = -2.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = -2.666666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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