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Simplifying 6x2 + -8x + -333 = 0 Reorder the terms: -333 + -8x + 6x2 = 0 Solving -333 + -8x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -55.5 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '55.5' to each side of the equation. -55.5 + -1.333333333x + 55.5 + x2 = 0 + 55.5 Reorder the terms: -55.5 + 55.5 + -1.333333333x + x2 = 0 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + -1.333333333x + x2 = 0 + 55.5 -1.333333333x + x2 = 0 + 55.5 Combine like terms: 0 + 55.5 = 55.5 -1.333333333x + x2 = 55.5 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 = 55.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 55.5 + 0.4444444442 Combine like terms: 55.5 + 0.4444444442 = 55.9444444442 0.4444444442 + -1.333333333x + x2 = 55.9444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 55.9444444442 Calculate the square root of the right side: 7.479601891 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 7.479601891 and -7.479601891.Subproblem 1
x + -0.6666666665 = 7.479601891 Simplifying x + -0.6666666665 = 7.479601891 Reorder the terms: -0.6666666665 + x = 7.479601891 Solving -0.6666666665 + x = 7.479601891 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 = 7.479601891 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 7.479601891 + 0.6666666665 x = 7.479601891 + 0.6666666665 Combine like terms: 7.479601891 + 0.6666666665 = 8.1462685575 x = 8.1462685575 Simplifying x = 8.1462685575Subproblem 2
x + -0.6666666665 = -7.479601891 Simplifying x + -0.6666666665 = -7.479601891 Reorder the terms: -0.6666666665 + x = -7.479601891 Solving -0.6666666665 + x = -7.479601891 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 = -7.479601891 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -7.479601891 + 0.6666666665 x = -7.479601891 + 0.6666666665 Combine like terms: -7.479601891 + 0.6666666665 = -6.8129352245 x = -6.8129352245 Simplifying x = -6.8129352245Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.1462685575, -6.8129352245}
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