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Simplifying -6x2 + 11x + 175 = 0 Reorder the terms: 175 + 11x + -6x2 = 0 Solving 175 + 11x + -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'. -29.16666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '29.16666667' to each side of the equation. -29.16666667 + -1.833333333x + 29.16666667 + x2 = 0 + 29.16666667 Reorder the terms: -29.16666667 + 29.16666667 + -1.833333333x + x2 = 0 + 29.16666667 Combine like terms: -29.16666667 + 29.16666667 = 0.00000000 0.00000000 + -1.833333333x + x2 = 0 + 29.16666667 -1.833333333x + x2 = 0 + 29.16666667 Combine like terms: 0 + 29.16666667 = 29.16666667 -1.833333333x + x2 = 29.16666667 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 = 29.16666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 29.16666667 + 0.8402777775 Combine like terms: 29.16666667 + 0.8402777775 = 30.0069444475 0.8402777775 + -1.833333333x + x2 = 30.0069444475 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 30.0069444475 Calculate the square root of the right side: 5.477859477 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 5.477859477 and -5.477859477.Subproblem 1
x + -0.9166666665 = 5.477859477 Simplifying x + -0.9166666665 = 5.477859477 Reorder the terms: -0.9166666665 + x = 5.477859477 Solving -0.9166666665 + x = 5.477859477 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 = 5.477859477 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 5.477859477 + 0.9166666665 x = 5.477859477 + 0.9166666665 Combine like terms: 5.477859477 + 0.9166666665 = 6.3945261435 x = 6.3945261435 Simplifying x = 6.3945261435Subproblem 2
x + -0.9166666665 = -5.477859477 Simplifying x + -0.9166666665 = -5.477859477 Reorder the terms: -0.9166666665 + x = -5.477859477 Solving -0.9166666665 + x = -5.477859477 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 = -5.477859477 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -5.477859477 + 0.9166666665 x = -5.477859477 + 0.9166666665 Combine like terms: -5.477859477 + 0.9166666665 = -4.5611928105 x = -4.5611928105 Simplifying x = -4.5611928105Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.3945261435, -4.5611928105}
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