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Simplifying x(0.8888888x + 0.222222) = 2.6 Reorder the terms: x(0.222222 + 0.8888888x) = 2.6 (0.222222 * x + 0.8888888x * x) = 2.6 (0.222222x + 0.8888888x2) = 2.6 Solving 0.222222x + 0.8888888x2 = 2.6 Solving for variable 'x'. Reorder the terms: -2.6 + 0.222222x + 0.8888888x2 = 2.6 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 -2.6 + 0.222222x + 0.8888888x2 = 0.0 Begin completing the square. Divide all terms by 0.8888888 the coefficient of the squared term: Divide each side by '0.8888888'. -2.925000293 + 0.249999775x + x2 = 0 Move the constant term to the right: Add '2.925000293' to each side of the equation. -2.925000293 + 0.249999775x + 2.925000293 + x2 = 0 + 2.925000293 Reorder the terms: -2.925000293 + 2.925000293 + 0.249999775x + x2 = 0 + 2.925000293 Combine like terms: -2.925000293 + 2.925000293 = 0.000000000 0.000000000 + 0.249999775x + x2 = 0 + 2.925000293 0.249999775x + x2 = 0 + 2.925000293 Combine like terms: 0 + 2.925000293 = 2.925000293 0.249999775x + x2 = 2.925000293 The x term is 0.249999775x. Take half its coefficient (0.1249998875). Square it (0.01562497188) and add it to both sides. Add '0.01562497188' to each side of the equation. 0.249999775x + 0.01562497188 + x2 = 2.925000293 + 0.01562497188 Reorder the terms: 0.01562497188 + 0.249999775x + x2 = 2.925000293 + 0.01562497188 Combine like terms: 2.925000293 + 0.01562497188 = 2.94062526488 0.01562497188 + 0.249999775x + x2 = 2.94062526488 Factor a perfect square on the left side: (x + 0.1249998875)(x + 0.1249998875) = 2.94062526488 Calculate the square root of the right side: 1.714825141 Break this problem into two subproblems by setting (x + 0.1249998875) equal to 1.714825141 and -1.714825141.Subproblem 1
x + 0.1249998875 = 1.714825141 Simplifying x + 0.1249998875 = 1.714825141 Reorder the terms: 0.1249998875 + x = 1.714825141 Solving 0.1249998875 + x = 1.714825141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1249998875' to each side of the equation. 0.1249998875 + -0.1249998875 + x = 1.714825141 + -0.1249998875 Combine like terms: 0.1249998875 + -0.1249998875 = 0.0000000000 0.0000000000 + x = 1.714825141 + -0.1249998875 x = 1.714825141 + -0.1249998875 Combine like terms: 1.714825141 + -0.1249998875 = 1.5898252535 x = 1.5898252535 Simplifying x = 1.5898252535Subproblem 2
x + 0.1249998875 = -1.714825141 Simplifying x + 0.1249998875 = -1.714825141 Reorder the terms: 0.1249998875 + x = -1.714825141 Solving 0.1249998875 + x = -1.714825141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1249998875' to each side of the equation. 0.1249998875 + -0.1249998875 + x = -1.714825141 + -0.1249998875 Combine like terms: 0.1249998875 + -0.1249998875 = 0.0000000000 0.0000000000 + x = -1.714825141 + -0.1249998875 x = -1.714825141 + -0.1249998875 Combine like terms: -1.714825141 + -0.1249998875 = -1.8398250285 x = -1.8398250285 Simplifying x = -1.8398250285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5898252535, -1.8398250285}
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