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Simplifying x2 + -0.6111111111111111x + 0.0555555555555556 = 0 Reorder the terms: 0.0555555555555556 + -0.6111111111111111x + x2 = 0 Solving 0.0555555555555556 + -0.6111111111111111x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0555555555555556' to each side of the equation. 0.0555555555555556 + -0.6111111111111111x + -0.0555555555555556 + x2 = 0 + -0.0555555555555556 Reorder the terms: 0.0555555555555556 + -0.0555555555555556 + -0.6111111111111111x + x2 = 0 + -0.0555555555555556 Combine like terms: 0.0555555555555556 + -0.0555555555555556 = 0.0000000000000000 0.0000000000000000 + -0.6111111111111111x + x2 = 0 + -0.0555555555555556 -0.6111111111111111x + x2 = 0 + -0.0555555555555556 Combine like terms: 0 + -0.0555555555555556 = -0.0555555555555556 -0.6111111111111111x + x2 = -0.0555555555555556 The x term is -0.6111111111111111x. Take half its coefficient (-0.3055555556). Square it (0.09336419756) and add it to both sides. Add '0.09336419756' to each side of the equation. -0.6111111111111111x + 0.09336419756 + x2 = -0.0555555555555556 + 0.09336419756 Reorder the terms: 0.09336419756 + -0.6111111111111111x + x2 = -0.0555555555555556 + 0.09336419756 Combine like terms: -0.0555555555555556 + 0.09336419756 = 0.0378086420044444 0.09336419756 + -0.6111111111111111x + x2 = 0.0378086420044444 Factor a perfect square on the left side: (x + -0.3055555556)(x + -0.3055555556) = 0.0378086420044444 Calculate the square root of the right side: 0.194444445 Break this problem into two subproblems by setting (x + -0.3055555556) equal to 0.194444445 and -0.194444445.Subproblem 1
x + -0.3055555556 = 0.194444445 Simplifying x + -0.3055555556 = 0.194444445 Reorder the terms: -0.3055555556 + x = 0.194444445 Solving -0.3055555556 + x = 0.194444445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3055555556' to each side of the equation. -0.3055555556 + 0.3055555556 + x = 0.194444445 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = 0.194444445 + 0.3055555556 x = 0.194444445 + 0.3055555556 Combine like terms: 0.194444445 + 0.3055555556 = 0.5000000006 x = 0.5000000006 Simplifying x = 0.5000000006Subproblem 2
x + -0.3055555556 = -0.194444445 Simplifying x + -0.3055555556 = -0.194444445 Reorder the terms: -0.3055555556 + x = -0.194444445 Solving -0.3055555556 + x = -0.194444445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3055555556' to each side of the equation. -0.3055555556 + 0.3055555556 + x = -0.194444445 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = -0.194444445 + 0.3055555556 x = -0.194444445 + 0.3055555556 Combine like terms: -0.194444445 + 0.3055555556 = 0.1111111106 x = 0.1111111106 Simplifying x = 0.1111111106Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5000000006, 0.1111111106}
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