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Simplifying 9x2 + -12x + -133 = 0 Reorder the terms: -133 + -12x + 9x2 = 0 Solving -133 + -12x + 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'. -14.77777778 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '14.77777778' to each side of the equation. -14.77777778 + -1.333333333x + 14.77777778 + x2 = 0 + 14.77777778 Reorder the terms: -14.77777778 + 14.77777778 + -1.333333333x + x2 = 0 + 14.77777778 Combine like terms: -14.77777778 + 14.77777778 = 0.00000000 0.00000000 + -1.333333333x + x2 = 0 + 14.77777778 -1.333333333x + x2 = 0 + 14.77777778 Combine like terms: 0 + 14.77777778 = 14.77777778 -1.333333333x + x2 = 14.77777778 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 14.77777778 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 14.77777778 + 0.4444444442 Combine like terms: 14.77777778 + 0.4444444442 = 15.2222222242 0.4444444442 + -1.333333333x + x2 = 15.2222222242 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 15.2222222242 Calculate the square root of the right side: 3.901566637 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 3.901566637 and -3.901566637.Subproblem 1
x + -0.6666666665 = 3.901566637 Simplifying x + -0.6666666665 = 3.901566637 Reorder the terms: -0.6666666665 + x = 3.901566637 Solving -0.6666666665 + x = 3.901566637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 3.901566637 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 3.901566637 + 0.6666666665 x = 3.901566637 + 0.6666666665 Combine like terms: 3.901566637 + 0.6666666665 = 4.5682333035 x = 4.5682333035 Simplifying x = 4.5682333035Subproblem 2
x + -0.6666666665 = -3.901566637 Simplifying x + -0.6666666665 = -3.901566637 Reorder the terms: -0.6666666665 + x = -3.901566637 Solving -0.6666666665 + x = -3.901566637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -3.901566637 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -3.901566637 + 0.6666666665 x = -3.901566637 + 0.6666666665 Combine like terms: -3.901566637 + 0.6666666665 = -3.2348999705 x = -3.2348999705 Simplifying x = -3.2348999705Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5682333035, -3.2348999705}
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