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Simplifying 9x2 + 20x + 8 = 0 Reorder the terms: 8 + 20x + 9x2 = 0 Solving 8 + 20x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 2.222222222x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 2.222222222x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 2.222222222x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 2.222222222x + x2 = 0 + -0.8888888889 2.222222222x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 2.222222222x + x2 = -0.8888888889 The x term is 2.222222222x. Take half its coefficient (1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. 2.222222222x + 1.234567901 + x2 = -0.8888888889 + 1.234567901 Reorder the terms: 1.234567901 + 2.222222222x + x2 = -0.8888888889 + 1.234567901 Combine like terms: -0.8888888889 + 1.234567901 = 0.3456790121 1.234567901 + 2.222222222x + x2 = 0.3456790121 Factor a perfect square on the left side: (x + 1.111111111)(x + 1.111111111) = 0.3456790121 Calculate the square root of the right side: 0.587944736 Break this problem into two subproblems by setting (x + 1.111111111) equal to 0.587944736 and -0.587944736.Subproblem 1
x + 1.111111111 = 0.587944736 Simplifying x + 1.111111111 = 0.587944736 Reorder the terms: 1.111111111 + x = 0.587944736 Solving 1.111111111 + x = 0.587944736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = 0.587944736 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = 0.587944736 + -1.111111111 x = 0.587944736 + -1.111111111 Combine like terms: 0.587944736 + -1.111111111 = -0.523166375 x = -0.523166375 Simplifying x = -0.523166375Subproblem 2
x + 1.111111111 = -0.587944736 Simplifying x + 1.111111111 = -0.587944736 Reorder the terms: 1.111111111 + x = -0.587944736 Solving 1.111111111 + x = -0.587944736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = -0.587944736 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = -0.587944736 + -1.111111111 x = -0.587944736 + -1.111111111 Combine like terms: -0.587944736 + -1.111111111 = -1.699055847 x = -1.699055847 Simplifying x = -1.699055847Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.523166375, -1.699055847}
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