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Simplifying (-2x2 + x + 6) + (5x2 + -4x + -2) = 0 Reorder the terms: (6 + x + -2x2) + (5x2 + -4x + -2) = 0 Remove parenthesis around (6 + x + -2x2) 6 + x + -2x2 + (5x2 + -4x + -2) = 0 Reorder the terms: 6 + x + -2x2 + (-2 + -4x + 5x2) = 0 Remove parenthesis around (-2 + -4x + 5x2) 6 + x + -2x2 + -2 + -4x + 5x2 = 0 Reorder the terms: 6 + -2 + x + -4x + -2x2 + 5x2 = 0 Combine like terms: 6 + -2 = 4 4 + x + -4x + -2x2 + 5x2 = 0 Combine like terms: x + -4x = -3x 4 + -3x + -2x2 + 5x2 = 0 Combine like terms: -2x2 + 5x2 = 3x2 4 + -3x + 3x2 = 0 Solving 4 + -3x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -1x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -1x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -1x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -1x + x2 = 0 + -1.333333333 -1x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -1x + x2 = -1.333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -1.333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1.333333333 + 0.25 Combine like terms: -1.333333333 + 0.25 = -1.083333333 0.25 + -1x + x2 = -1.083333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -1.083333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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