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Simplifying (6x2 + -5x + 4) + (-2x2 + 3x + 1) = 0 Reorder the terms: (4 + -5x + 6x2) + (-2x2 + 3x + 1) = 0 Remove parenthesis around (4 + -5x + 6x2) 4 + -5x + 6x2 + (-2x2 + 3x + 1) = 0 Reorder the terms: 4 + -5x + 6x2 + (1 + 3x + -2x2) = 0 Remove parenthesis around (1 + 3x + -2x2) 4 + -5x + 6x2 + 1 + 3x + -2x2 = 0 Reorder the terms: 4 + 1 + -5x + 3x + 6x2 + -2x2 = 0 Combine like terms: 4 + 1 = 5 5 + -5x + 3x + 6x2 + -2x2 = 0 Combine like terms: -5x + 3x = -2x 5 + -2x + 6x2 + -2x2 = 0 Combine like terms: 6x2 + -2x2 = 4x2 5 + -2x + 4x2 = 0 Solving 5 + -2x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -0.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -0.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -0.5x + x2 = 0 + -1.25 -0.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -0.5x + x2 = -1.25 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + -0.5x + x2 = -1.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -1.1875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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