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Simplifying (9x2) = 55x + 6 Reorder the terms: (9x2) = 6 + 55x Solving (9x2) = 6 + 55x Solving for variable 'x'. Reorder the terms: -6 + -55x + (9x2) = 6 + 55x + -6 + -55x Reorder the terms: -6 + -55x + (9x2) = 6 + -6 + 55x + -55x Combine like terms: 6 + -6 = 0 -6 + -55x + (9x2) = 0 + 55x + -55x -6 + -55x + (9x2) = 55x + -55x Combine like terms: 55x + -55x = 0 -6 + -55x + (9x2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + -6.111111111x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -6.111111111x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -6.111111111x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -6.111111111x + x2 = 0 + 0.6666666667 -6.111111111x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -6.111111111x + x2 = 0.6666666667 The x term is -6.111111111x. Take half its coefficient (-3.055555556). Square it (9.336419756) and add it to both sides. Add '9.336419756' to each side of the equation. -6.111111111x + 9.336419756 + x2 = 0.6666666667 + 9.336419756 Reorder the terms: 9.336419756 + -6.111111111x + x2 = 0.6666666667 + 9.336419756 Combine like terms: 0.6666666667 + 9.336419756 = 10.0030864227 9.336419756 + -6.111111111x + x2 = 10.0030864227 Factor a perfect square on the left side: ((x) + -3.055555556)((x) + -3.055555556) = 10.0030864227 Calculate the square root of the right side: 3.162765629 Break this problem into two subproblems by setting ((x) + -3.055555556) equal to 3.162765629 and -3.162765629.Subproblem 1
(x) + -3.055555556 = 3.162765629 Simplifying (x) + -3.055555556 = 3.162765629 x + -3.055555556 = 3.162765629 Reorder the terms: -3.055555556 + x = 3.162765629 Solving -3.055555556 + x = 3.162765629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.055555556' to each side of the equation. -3.055555556 + 3.055555556 + x = 3.162765629 + 3.055555556 Combine like terms: -3.055555556 + 3.055555556 = 0.000000000 0.000000000 + x = 3.162765629 + 3.055555556 x = 3.162765629 + 3.055555556 Combine like terms: 3.162765629 + 3.055555556 = 6.218321185 x = 6.218321185 Simplifying x = 6.218321185Subproblem 2
(x) + -3.055555556 = -3.162765629 Simplifying (x) + -3.055555556 = -3.162765629 x + -3.055555556 = -3.162765629 Reorder the terms: -3.055555556 + x = -3.162765629 Solving -3.055555556 + x = -3.162765629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.055555556' to each side of the equation. -3.055555556 + 3.055555556 + x = -3.162765629 + 3.055555556 Combine like terms: -3.055555556 + 3.055555556 = 0.000000000 0.000000000 + x = -3.162765629 + 3.055555556 x = -3.162765629 + 3.055555556 Combine like terms: -3.162765629 + 3.055555556 = -0.107210073 x = -0.107210073 Simplifying x = -0.107210073Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.218321185, -0.107210073}
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