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Simplifying 9x2 + -38x + 23 = 0 Reorder the terms: 23 + -38x + 9x2 = 0 Solving 23 + -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'. 2.555555556 + -4.222222222x + x2 = 0 Move the constant term to the right: Add '-2.555555556' to each side of the equation. 2.555555556 + -4.222222222x + -2.555555556 + x2 = 0 + -2.555555556 Reorder the terms: 2.555555556 + -2.555555556 + -4.222222222x + x2 = 0 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + -4.222222222x + x2 = 0 + -2.555555556 -4.222222222x + x2 = 0 + -2.555555556 Combine like terms: 0 + -2.555555556 = -2.555555556 -4.222222222x + x2 = -2.555555556 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 = -2.555555556 + 4.456790123 Reorder the terms: 4.456790123 + -4.222222222x + x2 = -2.555555556 + 4.456790123 Combine like terms: -2.555555556 + 4.456790123 = 1.901234567 4.456790123 + -4.222222222x + x2 = 1.901234567 Factor a perfect square on the left side: (x + -2.111111111)(x + -2.111111111) = 1.901234567 Calculate the square root of the right side: 1.378852627 Break this problem into two subproblems by setting (x + -2.111111111) equal to 1.378852627 and -1.378852627.Subproblem 1
x + -2.111111111 = 1.378852627 Simplifying x + -2.111111111 = 1.378852627 Reorder the terms: -2.111111111 + x = 1.378852627 Solving -2.111111111 + x = 1.378852627 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 = 1.378852627 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = 1.378852627 + 2.111111111 x = 1.378852627 + 2.111111111 Combine like terms: 1.378852627 + 2.111111111 = 3.489963738 x = 3.489963738 Simplifying x = 3.489963738Subproblem 2
x + -2.111111111 = -1.378852627 Simplifying x + -2.111111111 = -1.378852627 Reorder the terms: -2.111111111 + x = -1.378852627 Solving -2.111111111 + x = -1.378852627 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 = -1.378852627 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = -1.378852627 + 2.111111111 x = -1.378852627 + 2.111111111 Combine like terms: -1.378852627 + 2.111111111 = 0.732258484 x = 0.732258484 Simplifying x = 0.732258484Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.489963738, 0.732258484}
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