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Simplifying (5x2 + 5x + 8) + (8x2 + 8x) = 0 Reorder the terms: (8 + 5x + 5x2) + (8x2 + 8x) = 0 Remove parenthesis around (8 + 5x + 5x2) 8 + 5x + 5x2 + (8x2 + 8x) = 0 Reorder the terms: 8 + 5x + 5x2 + (8x + 8x2) = 0 Remove parenthesis around (8x + 8x2) 8 + 5x + 5x2 + 8x + 8x2 = 0 Reorder the terms: 8 + 5x + 8x + 5x2 + 8x2 = 0 Combine like terms: 5x + 8x = 13x 8 + 13x + 5x2 + 8x2 = 0 Combine like terms: 5x2 + 8x2 = 13x2 8 + 13x + 13x2 = 0 Solving 8 + 13x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.6153846154 + x + x2 = 0 Move the constant term to the right: Add '-0.6153846154' to each side of the equation. 0.6153846154 + x + -0.6153846154 + x2 = 0 + -0.6153846154 Reorder the terms: 0.6153846154 + -0.6153846154 + x + x2 = 0 + -0.6153846154 Combine like terms: 0.6153846154 + -0.6153846154 = 0.0000000000 0.0000000000 + x + x2 = 0 + -0.6153846154 x + x2 = 0 + -0.6153846154 Combine like terms: 0 + -0.6153846154 = -0.6153846154 x + x2 = -0.6153846154 The x term is x. 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. + 0.25 + x2 = -0.6153846154 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.6153846154 + 0.25 Combine like terms: -0.6153846154 + 0.25 = -0.3653846154 1.25 + x2 = -0.3653846154 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.3653846154 Can't calculate square root of the right side. The solution to this equation could not be determined.
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