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Simplifying 3 + 8x = 3x(2x + -1) Reorder the terms: 3 + 8x = 3x(-1 + 2x) 3 + 8x = (-1 * 3x + 2x * 3x) 3 + 8x = (-3x + 6x2) Solving 3 + 8x = -3x + 6x2 Solving for variable 'x'. Combine like terms: 8x + 3x = 11x 3 + 11x + -6x2 = -3x + 6x2 + 3x + -6x2 Reorder the terms: 3 + 11x + -6x2 = -3x + 3x + 6x2 + -6x2 Combine like terms: -3x + 3x = 0 3 + 11x + -6x2 = 0 + 6x2 + -6x2 3 + 11x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 3 + 11x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.5 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.833333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.833333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.833333333x + x2 = 0 + 0.5 -1.833333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.833333333x + x2 = 0.5 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = 0.5 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 0.5 + 0.8402777775 Combine like terms: 0.5 + 0.8402777775 = 1.3402777775 0.8402777775 + -1.833333333x + x2 = 1.3402777775 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 1.3402777775 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 1.157703666 and -1.157703666.Subproblem 1
x + -0.9166666665 = 1.157703666 Simplifying x + -0.9166666665 = 1.157703666 Reorder the terms: -0.9166666665 + x = 1.157703666 Solving -0.9166666665 + x = 1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 1.157703666 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.157703666 + 0.9166666665 x = 1.157703666 + 0.9166666665 Combine like terms: 1.157703666 + 0.9166666665 = 2.0743703325 x = 2.0743703325 Simplifying x = 2.0743703325Subproblem 2
x + -0.9166666665 = -1.157703666 Simplifying x + -0.9166666665 = -1.157703666 Reorder the terms: -0.9166666665 + x = -1.157703666 Solving -0.9166666665 + x = -1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -1.157703666 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.157703666 + 0.9166666665 x = -1.157703666 + 0.9166666665 Combine like terms: -1.157703666 + 0.9166666665 = -0.2410369995 x = -0.2410369995 Simplifying x = -0.2410369995Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0743703325, -0.2410369995}
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