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Simplifying 9x2 + -38x + -8 = 0 Reorder the terms: -8 + -38x + 9x2 = 0 Solving -8 + -38x + 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 + -4.222222222x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -4.222222222x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -4.222222222x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -4.222222222x + x2 = 0 + 0.8888888889 -4.222222222x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -4.222222222x + x2 = 0.8888888889 The x term is -4.222222222x. Take half its coefficient (-2.111111111). Square it (4.456790123) and add it to both sides. Add '4.456790123' to each side of the equation. -4.222222222x + 4.456790123 + x2 = 0.8888888889 + 4.456790123 Reorder the terms: 4.456790123 + -4.222222222x + x2 = 0.8888888889 + 4.456790123 Combine like terms: 0.8888888889 + 4.456790123 = 5.3456790119 4.456790123 + -4.222222222x + x2 = 5.3456790119 Factor a perfect square on the left side: (x + -2.111111111)(x + -2.111111111) = 5.3456790119 Calculate the square root of the right side: 2.31207245 Break this problem into two subproblems by setting (x + -2.111111111) equal to 2.31207245 and -2.31207245.Subproblem 1
x + -2.111111111 = 2.31207245 Simplifying x + -2.111111111 = 2.31207245 Reorder the terms: -2.111111111 + x = 2.31207245 Solving -2.111111111 + x = 2.31207245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.111111111' to each side of the equation. -2.111111111 + 2.111111111 + x = 2.31207245 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = 2.31207245 + 2.111111111 x = 2.31207245 + 2.111111111 Combine like terms: 2.31207245 + 2.111111111 = 4.423183561 x = 4.423183561 Simplifying x = 4.423183561Subproblem 2
x + -2.111111111 = -2.31207245 Simplifying x + -2.111111111 = -2.31207245 Reorder the terms: -2.111111111 + x = -2.31207245 Solving -2.111111111 + x = -2.31207245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.111111111' to each side of the equation. -2.111111111 + 2.111111111 + x = -2.31207245 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = -2.31207245 + 2.111111111 x = -2.31207245 + 2.111111111 Combine like terms: -2.31207245 + 2.111111111 = -0.200961339 x = -0.200961339 Simplifying x = -0.200961339Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.423183561, -0.200961339}
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