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Simplifying 23x2 + 384x + -15590 = 0 Reorder the terms: -15590 + 384x + 23x2 = 0 Solving -15590 + 384x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -677.826087 + 16.69565217x + x2 = 0 Move the constant term to the right: Add '677.826087' to each side of the equation. -677.826087 + 16.69565217x + 677.826087 + x2 = 0 + 677.826087 Reorder the terms: -677.826087 + 677.826087 + 16.69565217x + x2 = 0 + 677.826087 Combine like terms: -677.826087 + 677.826087 = 0.000000 0.000000 + 16.69565217x + x2 = 0 + 677.826087 16.69565217x + x2 = 0 + 677.826087 Combine like terms: 0 + 677.826087 = 677.826087 16.69565217x + x2 = 677.826087 The x term is 16.69565217x. Take half its coefficient (8.347826085). Square it (69.68620035) and add it to both sides. Add '69.68620035' to each side of the equation. 16.69565217x + 69.68620035 + x2 = 677.826087 + 69.68620035 Reorder the terms: 69.68620035 + 16.69565217x + x2 = 677.826087 + 69.68620035 Combine like terms: 677.826087 + 69.68620035 = 747.51228735 69.68620035 + 16.69565217x + x2 = 747.51228735 Factor a perfect square on the left side: (x + 8.347826085)(x + 8.347826085) = 747.51228735 Calculate the square root of the right side: 27.340670938 Break this problem into two subproblems by setting (x + 8.347826085) equal to 27.340670938 and -27.340670938.Subproblem 1
x + 8.347826085 = 27.340670938 Simplifying x + 8.347826085 = 27.340670938 Reorder the terms: 8.347826085 + x = 27.340670938 Solving 8.347826085 + x = 27.340670938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.347826085' to each side of the equation. 8.347826085 + -8.347826085 + x = 27.340670938 + -8.347826085 Combine like terms: 8.347826085 + -8.347826085 = 0.000000000 0.000000000 + x = 27.340670938 + -8.347826085 x = 27.340670938 + -8.347826085 Combine like terms: 27.340670938 + -8.347826085 = 18.992844853 x = 18.992844853 Simplifying x = 18.992844853Subproblem 2
x + 8.347826085 = -27.340670938 Simplifying x + 8.347826085 = -27.340670938 Reorder the terms: 8.347826085 + x = -27.340670938 Solving 8.347826085 + x = -27.340670938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.347826085' to each side of the equation. 8.347826085 + -8.347826085 + x = -27.340670938 + -8.347826085 Combine like terms: 8.347826085 + -8.347826085 = 0.000000000 0.000000000 + x = -27.340670938 + -8.347826085 x = -27.340670938 + -8.347826085 Combine like terms: -27.340670938 + -8.347826085 = -35.688497023 x = -35.688497023 Simplifying x = -35.688497023Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.992844853, -35.688497023}
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