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Simplifying (3x2 + 5x + 5) + (5x2 + 7x) = 0 Reorder the terms: (5 + 5x + 3x2) + (5x2 + 7x) = 0 Remove parenthesis around (5 + 5x + 3x2) 5 + 5x + 3x2 + (5x2 + 7x) = 0 Reorder the terms: 5 + 5x + 3x2 + (7x + 5x2) = 0 Remove parenthesis around (7x + 5x2) 5 + 5x + 3x2 + 7x + 5x2 = 0 Reorder the terms: 5 + 5x + 7x + 3x2 + 5x2 = 0 Combine like terms: 5x + 7x = 12x 5 + 12x + 3x2 + 5x2 = 0 Combine like terms: 3x2 + 5x2 = 8x2 5 + 12x + 8x2 = 0 Solving 5 + 12x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 1.5x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 1.5x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 1.5x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 1.5x + x2 = 0 + -0.625 1.5x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 1.5x + x2 = -0.625 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -0.625 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -0.625 + 0.5625 Combine like terms: -0.625 + 0.5625 = -0.0625 0.5625 + 1.5x + x2 = -0.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.0625 Can't calculate square root of the right side. The solution to this equation could not be determined.
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