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Simplifying 3x2 + -4x + -24 = 0 Reorder the terms: -24 + -4x + 3x2 = 0 Solving -24 + -4x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -1.333333333x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -1.333333333x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1.333333333x + x2 = 0 + 8 -1.333333333x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1.333333333x + x2 = 8 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 = 8 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 8 + 0.4444444442 Combine like terms: 8 + 0.4444444442 = 8.4444444442 0.4444444442 + -1.333333333x + x2 = 8.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 8.4444444442 Calculate the square root of the right side: 2.905932629 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.905932629 and -2.905932629.Subproblem 1
x + -0.6666666665 = 2.905932629 Simplifying x + -0.6666666665 = 2.905932629 Reorder the terms: -0.6666666665 + x = 2.905932629 Solving -0.6666666665 + x = 2.905932629 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 = 2.905932629 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.905932629 + 0.6666666665 x = 2.905932629 + 0.6666666665 Combine like terms: 2.905932629 + 0.6666666665 = 3.5725992955 x = 3.5725992955 Simplifying x = 3.5725992955Subproblem 2
x + -0.6666666665 = -2.905932629 Simplifying x + -0.6666666665 = -2.905932629 Reorder the terms: -0.6666666665 + x = -2.905932629 Solving -0.6666666665 + x = -2.905932629 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 = -2.905932629 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.905932629 + 0.6666666665 x = -2.905932629 + 0.6666666665 Combine like terms: -2.905932629 + 0.6666666665 = -2.2392659625 x = -2.2392659625 Simplifying x = -2.2392659625Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5725992955, -2.2392659625}
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