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Simplifying 23x2 + -15 = 6x Reorder the terms: -15 + 23x2 = 6x Solving -15 + 23x2 = 6x Solving for variable 'x'. Reorder the terms: -15 + -6x + 23x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -15 + -6x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.652173913 + -0.2608695652x + x2 = 0 Move the constant term to the right: Add '0.652173913' to each side of the equation. -0.652173913 + -0.2608695652x + 0.652173913 + x2 = 0 + 0.652173913 Reorder the terms: -0.652173913 + 0.652173913 + -0.2608695652x + x2 = 0 + 0.652173913 Combine like terms: -0.652173913 + 0.652173913 = 0.000000000 0.000000000 + -0.2608695652x + x2 = 0 + 0.652173913 -0.2608695652x + x2 = 0 + 0.652173913 Combine like terms: 0 + 0.652173913 = 0.652173913 -0.2608695652x + x2 = 0.652173913 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 = 0.652173913 + 0.01701323251 Reorder the terms: 0.01701323251 + -0.2608695652x + x2 = 0.652173913 + 0.01701323251 Combine like terms: 0.652173913 + 0.01701323251 = 0.66918714551 0.01701323251 + -0.2608695652x + x2 = 0.66918714551 Factor a perfect square on the left side: (x + -0.1304347826)(x + -0.1304347826) = 0.66918714551 Calculate the square root of the right side: 0.818038597 Break this problem into two subproblems by setting (x + -0.1304347826) equal to 0.818038597 and -0.818038597.Subproblem 1
x + -0.1304347826 = 0.818038597 Simplifying x + -0.1304347826 = 0.818038597 Reorder the terms: -0.1304347826 + x = 0.818038597 Solving -0.1304347826 + x = 0.818038597 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 = 0.818038597 + 0.1304347826 Combine like terms: -0.1304347826 + 0.1304347826 = 0.0000000000 0.0000000000 + x = 0.818038597 + 0.1304347826 x = 0.818038597 + 0.1304347826 Combine like terms: 0.818038597 + 0.1304347826 = 0.9484733796 x = 0.9484733796 Simplifying x = 0.9484733796Subproblem 2
x + -0.1304347826 = -0.818038597 Simplifying x + -0.1304347826 = -0.818038597 Reorder the terms: -0.1304347826 + x = -0.818038597 Solving -0.1304347826 + x = -0.818038597 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 = -0.818038597 + 0.1304347826 Combine like terms: -0.1304347826 + 0.1304347826 = 0.0000000000 0.0000000000 + x = -0.818038597 + 0.1304347826 x = -0.818038597 + 0.1304347826 Combine like terms: -0.818038597 + 0.1304347826 = -0.6876038144 x = -0.6876038144 Simplifying x = -0.6876038144Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9484733796, -0.6876038144}
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