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Simplifying 441x2 + -588x + 184 = 0 Reorder the terms: 184 + -588x + 441x2 = 0 Solving 184 + -588x + 441x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 441 the coefficient of the squared term: Divide each side by '441'. 0.4172335601 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.4172335601' to each side of the equation. 0.4172335601 + -1.333333333x + -0.4172335601 + x2 = 0 + -0.4172335601 Reorder the terms: 0.4172335601 + -0.4172335601 + -1.333333333x + x2 = 0 + -0.4172335601 Combine like terms: 0.4172335601 + -0.4172335601 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + -0.4172335601 -1.333333333x + x2 = 0 + -0.4172335601 Combine like terms: 0 + -0.4172335601 = -0.4172335601 -1.333333333x + x2 = -0.4172335601 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 = -0.4172335601 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.4172335601 + 0.4444444442 Combine like terms: -0.4172335601 + 0.4444444442 = 0.0272108841 0.4444444442 + -1.333333333x + x2 = 0.0272108841 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.0272108841 Calculate the square root of the right side: 0.164957219 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.164957219 and -0.164957219.Subproblem 1
x + -0.6666666665 = 0.164957219 Simplifying x + -0.6666666665 = 0.164957219 Reorder the terms: -0.6666666665 + x = 0.164957219 Solving -0.6666666665 + x = 0.164957219 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 = 0.164957219 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.164957219 + 0.6666666665 x = 0.164957219 + 0.6666666665 Combine like terms: 0.164957219 + 0.6666666665 = 0.8316238855 x = 0.8316238855 Simplifying x = 0.8316238855Subproblem 2
x + -0.6666666665 = -0.164957219 Simplifying x + -0.6666666665 = -0.164957219 Reorder the terms: -0.6666666665 + x = -0.164957219 Solving -0.6666666665 + x = -0.164957219 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 = -0.164957219 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.164957219 + 0.6666666665 x = -0.164957219 + 0.6666666665 Combine like terms: -0.164957219 + 0.6666666665 = 0.5017094475 x = 0.5017094475 Simplifying x = 0.5017094475Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8316238855, 0.5017094475}
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