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Simplifying (x2 + 2x + 1) + (4x2 + 5x + 3) = 0 Reorder the terms: (1 + 2x + x2) + (4x2 + 5x + 3) = 0 Remove parenthesis around (1 + 2x + x2) 1 + 2x + x2 + (4x2 + 5x + 3) = 0 Reorder the terms: 1 + 2x + x2 + (3 + 5x + 4x2) = 0 Remove parenthesis around (3 + 5x + 4x2) 1 + 2x + x2 + 3 + 5x + 4x2 = 0 Reorder the terms: 1 + 3 + 2x + 5x + x2 + 4x2 = 0 Combine like terms: 1 + 3 = 4 4 + 2x + 5x + x2 + 4x2 = 0 Combine like terms: 2x + 5x = 7x 4 + 7x + x2 + 4x2 = 0 Combine like terms: x2 + 4x2 = 5x2 4 + 7x + 5x2 = 0 Solving 4 + 7x + 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'. 0.8 + 1.4x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 1.4x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 1.4x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 1.4x + x2 = 0 + -0.8 1.4x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 1.4x + x2 = -0.8 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -0.8 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -0.8 + 0.49 Combine like terms: -0.8 + 0.49 = -0.31 0.49 + 1.4x + x2 = -0.31 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -0.31 Can't calculate square root of the right side. The solution to this equation could not be determined.
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