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Simplifying 9x2 + 55x + -6 = 0 Reorder the terms: -6 + 55x + 9x2 = 0 Solving -6 + 55x + 9x2 = 0 Solving for variable 'x'. 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 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 = 0.107210073Subproblem 2
x + 3.055555556 = -3.162765629 Simplifying 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 = -6.218321185Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.107210073, -6.218321185}
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