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Simplifying 9x2 + 12x + -2 = 0 Reorder the terms: -2 + 12x + 9x2 = 0 Solving -2 + 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'. -0.2222222222 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 1.333333333x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 1.333333333x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.2222222222 1.333333333x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 1.333333333x + x2 = 0.2222222222 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 = 0.2222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.2222222222 + 0.4444444442 Combine like terms: 0.2222222222 + 0.4444444442 = 0.6666666664 0.4444444442 + 1.333333333x + x2 = 0.6666666664 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.6666666664 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.816496581 and -0.816496581.Subproblem 1
x + 0.6666666665 = 0.816496581 Simplifying x + 0.6666666665 = 0.816496581 Reorder the terms: 0.6666666665 + x = 0.816496581 Solving 0.6666666665 + x = 0.816496581 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 = 0.816496581 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.816496581 + -0.6666666665 x = 0.816496581 + -0.6666666665 Combine like terms: 0.816496581 + -0.6666666665 = 0.1498299145 x = 0.1498299145 Simplifying x = 0.1498299145Subproblem 2
x + 0.6666666665 = -0.816496581 Simplifying x + 0.6666666665 = -0.816496581 Reorder the terms: 0.6666666665 + x = -0.816496581 Solving 0.6666666665 + x = -0.816496581 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 = -0.816496581 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.816496581 + -0.6666666665 x = -0.816496581 + -0.6666666665 Combine like terms: -0.816496581 + -0.6666666665 = -1.4831632475 x = -1.4831632475 Simplifying x = -1.4831632475Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1498299145, -1.4831632475}
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