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Simplifying 9x2 + -12x + -122 = 0 Reorder the terms: -122 + -12x + 9x2 = 0 Solving -122 + -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'. -13.55555556 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '13.55555556' to each side of the equation. -13.55555556 + -1.333333333x + 13.55555556 + x2 = 0 + 13.55555556 Reorder the terms: -13.55555556 + 13.55555556 + -1.333333333x + x2 = 0 + 13.55555556 Combine like terms: -13.55555556 + 13.55555556 = 0.00000000 0.00000000 + -1.333333333x + x2 = 0 + 13.55555556 -1.333333333x + x2 = 0 + 13.55555556 Combine like terms: 0 + 13.55555556 = 13.55555556 -1.333333333x + x2 = 13.55555556 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 = 13.55555556 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 13.55555556 + 0.4444444442 Combine like terms: 13.55555556 + 0.4444444442 = 14.0000000042 0.4444444442 + -1.333333333x + x2 = 14.0000000042 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 14.0000000042 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -0.6666666665 = 3.741657387 Simplifying x + -0.6666666665 = 3.741657387 Reorder the terms: -0.6666666665 + x = 3.741657387 Solving -0.6666666665 + x = 3.741657387 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 = 3.741657387 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 3.741657387 + 0.6666666665 x = 3.741657387 + 0.6666666665 Combine like terms: 3.741657387 + 0.6666666665 = 4.4083240535 x = 4.4083240535 Simplifying x = 4.4083240535Subproblem 2
x + -0.6666666665 = -3.741657387 Simplifying x + -0.6666666665 = -3.741657387 Reorder the terms: -0.6666666665 + x = -3.741657387 Solving -0.6666666665 + x = -3.741657387 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 = -3.741657387 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -3.741657387 + 0.6666666665 x = -3.741657387 + 0.6666666665 Combine like terms: -3.741657387 + 0.6666666665 = -3.0749907205 x = -3.0749907205 Simplifying x = -3.0749907205Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4083240535, -3.0749907205}
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