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Simplifying (2x2 + 2x + 1) + (3x2 + -5x + 6) = 0 Reorder the terms: (1 + 2x + 2x2) + (3x2 + -5x + 6) = 0 Remove parenthesis around (1 + 2x + 2x2) 1 + 2x + 2x2 + (3x2 + -5x + 6) = 0 Reorder the terms: 1 + 2x + 2x2 + (6 + -5x + 3x2) = 0 Remove parenthesis around (6 + -5x + 3x2) 1 + 2x + 2x2 + 6 + -5x + 3x2 = 0 Reorder the terms: 1 + 6 + 2x + -5x + 2x2 + 3x2 = 0 Combine like terms: 1 + 6 = 7 7 + 2x + -5x + 2x2 + 3x2 = 0 Combine like terms: 2x + -5x = -3x 7 + -3x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 7 + -3x + 5x2 = 0 Solving 7 + -3x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -0.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -0.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -0.6x + x2 = 0 + -1.4 -0.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -0.6x + x2 = -1.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = -1.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -1.4 + 0.09 Combine like terms: -1.4 + 0.09 = -1.31 0.09 + -0.6x + x2 = -1.31 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = -1.31 Can't calculate square root of the right side. The solution to this equation could not be determined.
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