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Simplifying -9x2 + -198x + 108 = 0 Reorder the terms: 108 + -198x + -9x2 = 0 Solving 108 + -198x + -9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(12 + -22x + -1x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(12 + -22x + -1x2)' equal to zero and attempt to solve: Simplifying 12 + -22x + -1x2 = 0 Solving 12 + -22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 22x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 22x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 22x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 22x + x2 = 0 + 12 22x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 22x + x2 = 12 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 12 + 121 Reorder the terms: 121 + 22x + x2 = 12 + 121 Combine like terms: 12 + 121 = 133 121 + 22x + x2 = 133 Factor a perfect square on the left side: (x + 11)(x + 11) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + 11) equal to 11.532562595 and -11.532562595.Subproblem 1
x + 11 = 11.532562595 Simplifying x + 11 = 11.532562595 Reorder the terms: 11 + x = 11.532562595 Solving 11 + x = 11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 11.532562595 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.532562595 + -11 x = 11.532562595 + -11 Combine like terms: 11.532562595 + -11 = 0.532562595 x = 0.532562595 Simplifying x = 0.532562595Subproblem 2
x + 11 = -11.532562595 Simplifying x + 11 = -11.532562595 Reorder the terms: 11 + x = -11.532562595 Solving 11 + x = -11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -11.532562595 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.532562595 + -11 x = -11.532562595 + -11 Combine like terms: -11.532562595 + -11 = -22.532562595 x = -22.532562595 Simplifying x = -22.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.532562595, -22.532562595}Solution
x = {0.532562595, -22.532562595}
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