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Simplifying (6x2 + 5x + 1) + (2x2 + 8x) = 0 Reorder the terms: (1 + 5x + 6x2) + (2x2 + 8x) = 0 Remove parenthesis around (1 + 5x + 6x2) 1 + 5x + 6x2 + (2x2 + 8x) = 0 Reorder the terms: 1 + 5x + 6x2 + (8x + 2x2) = 0 Remove parenthesis around (8x + 2x2) 1 + 5x + 6x2 + 8x + 2x2 = 0 Reorder the terms: 1 + 5x + 8x + 6x2 + 2x2 = 0 Combine like terms: 5x + 8x = 13x 1 + 13x + 6x2 + 2x2 = 0 Combine like terms: 6x2 + 2x2 = 8x2 1 + 13x + 8x2 = 0 Solving 1 + 13x + 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'. 0.125 + 1.625x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 1.625x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 1.625x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 1.625x + x2 = 0 + -0.125 1.625x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 1.625x + x2 = -0.125 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = -0.125 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = -0.125 + 0.66015625 Combine like terms: -0.125 + 0.66015625 = 0.53515625 0.66015625 + 1.625x + x2 = 0.53515625 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = 0.53515625 Calculate the square root of the right side: 0.731543744 Break this problem into two subproblems by setting (x + 0.8125) equal to 0.731543744 and -0.731543744.Subproblem 1
x + 0.8125 = 0.731543744 Simplifying x + 0.8125 = 0.731543744 Reorder the terms: 0.8125 + x = 0.731543744 Solving 0.8125 + x = 0.731543744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = 0.731543744 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = 0.731543744 + -0.8125 x = 0.731543744 + -0.8125 Combine like terms: 0.731543744 + -0.8125 = -0.080956256 x = -0.080956256 Simplifying x = -0.080956256Subproblem 2
x + 0.8125 = -0.731543744 Simplifying x + 0.8125 = -0.731543744 Reorder the terms: 0.8125 + x = -0.731543744 Solving 0.8125 + x = -0.731543744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = -0.731543744 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = -0.731543744 + -0.8125 x = -0.731543744 + -0.8125 Combine like terms: -0.731543744 + -0.8125 = -1.544043744 x = -1.544043744 Simplifying x = -1.544043744Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.080956256, -1.544043744}
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