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Simplifying 23x2 + 6x + -120 = 0 Reorder the terms: -120 + 6x + 23x2 = 0 Solving -120 + 6x + 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'. -5.217391304 + 0.2608695652x + x2 = 0 Move the constant term to the right: Add '5.217391304' to each side of the equation. -5.217391304 + 0.2608695652x + 5.217391304 + x2 = 0 + 5.217391304 Reorder the terms: -5.217391304 + 5.217391304 + 0.2608695652x + x2 = 0 + 5.217391304 Combine like terms: -5.217391304 + 5.217391304 = 0.000000000 0.000000000 + 0.2608695652x + x2 = 0 + 5.217391304 0.2608695652x + x2 = 0 + 5.217391304 Combine like terms: 0 + 5.217391304 = 5.217391304 0.2608695652x + x2 = 5.217391304 The x term is 0.2608695652x. Take half its coefficient (0.1304347826). Square it (0.01701323251) and add it to both sides. Add '0.01701323251' to each side of the equation. 0.2608695652x + 0.01701323251 + x2 = 5.217391304 + 0.01701323251 Reorder the terms: 0.01701323251 + 0.2608695652x + x2 = 5.217391304 + 0.01701323251 Combine like terms: 5.217391304 + 0.01701323251 = 5.23440453651 0.01701323251 + 0.2608695652x + x2 = 5.23440453651 Factor a perfect square on the left side: (x + 0.1304347826)(x + 0.1304347826) = 5.23440453651 Calculate the square root of the right side: 2.287882107 Break this problem into two subproblems by setting (x + 0.1304347826) equal to 2.287882107 and -2.287882107.Subproblem 1
x + 0.1304347826 = 2.287882107 Simplifying x + 0.1304347826 = 2.287882107 Reorder the terms: 0.1304347826 + x = 2.287882107 Solving 0.1304347826 + x = 2.287882107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1304347826' to each side of the equation. 0.1304347826 + -0.1304347826 + x = 2.287882107 + -0.1304347826 Combine like terms: 0.1304347826 + -0.1304347826 = 0.0000000000 0.0000000000 + x = 2.287882107 + -0.1304347826 x = 2.287882107 + -0.1304347826 Combine like terms: 2.287882107 + -0.1304347826 = 2.1574473244 x = 2.1574473244 Simplifying x = 2.1574473244Subproblem 2
x + 0.1304347826 = -2.287882107 Simplifying x + 0.1304347826 = -2.287882107 Reorder the terms: 0.1304347826 + x = -2.287882107 Solving 0.1304347826 + x = -2.287882107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1304347826' to each side of the equation. 0.1304347826 + -0.1304347826 + x = -2.287882107 + -0.1304347826 Combine like terms: 0.1304347826 + -0.1304347826 = 0.0000000000 0.0000000000 + x = -2.287882107 + -0.1304347826 x = -2.287882107 + -0.1304347826 Combine like terms: -2.287882107 + -0.1304347826 = -2.4183168896 x = -2.4183168896 Simplifying x = -2.4183168896Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1574473244, -2.4183168896}
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