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Simplifying 18x2 + 24x + -1 = 0 Reorder the terms: -1 + 24x + 18x2 = 0 Solving -1 + 24x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 1.333333333x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 1.333333333x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 1.333333333x + x2 = 0 + 0.05555555556 1.333333333x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 1.333333333x + x2 = 0.05555555556 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 = 0.05555555556 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.05555555556 + 0.4444444442 Combine like terms: 0.05555555556 + 0.4444444442 = 0.49999999976 0.4444444442 + 1.333333333x + x2 = 0.49999999976 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.49999999976 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.707106781 and -0.707106781.Subproblem 1
x + 0.6666666665 = 0.707106781 Simplifying x + 0.6666666665 = 0.707106781 Reorder the terms: 0.6666666665 + x = 0.707106781 Solving 0.6666666665 + x = 0.707106781 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 = 0.707106781 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.707106781 + -0.6666666665 x = 0.707106781 + -0.6666666665 Combine like terms: 0.707106781 + -0.6666666665 = 0.0404401145 x = 0.0404401145 Simplifying x = 0.0404401145Subproblem 2
x + 0.6666666665 = -0.707106781 Simplifying x + 0.6666666665 = -0.707106781 Reorder the terms: 0.6666666665 + x = -0.707106781 Solving 0.6666666665 + x = -0.707106781 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 = -0.707106781 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.707106781 + -0.6666666665 x = -0.707106781 + -0.6666666665 Combine like terms: -0.707106781 + -0.6666666665 = -1.3737734475 x = -1.3737734475 Simplifying x = -1.3737734475Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0404401145, -1.3737734475}
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