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Simplifying 0 = 9x2 + -20x + 8 Reorder the terms: 0 = 8 + -20x + 9x2 Solving 0 = 8 + -20x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 20x + -9x2 = 8 + -20x + 9x2 + -8 + 20x + -9x2 Reorder the terms: -8 + 20x + -9x2 = 8 + -8 + -20x + 20x + 9x2 + -9x2 Combine like terms: 8 + -8 = 0 -8 + 20x + -9x2 = 0 + -20x + 20x + 9x2 + -9x2 -8 + 20x + -9x2 = -20x + 20x + 9x2 + -9x2 Combine like terms: -20x + 20x = 0 -8 + 20x + -9x2 = 0 + 9x2 + -9x2 -8 + 20x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -8 + 20x + -9x2 = 0 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 = 1.699055847 x = 1.699055847 Simplifying x = 1.699055847Subproblem 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 = 0.523166375 x = 0.523166375 Simplifying x = 0.523166375Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.699055847, 0.523166375}
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