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Simplifying 6x2 + 11x + -22 = 0 Reorder the terms: -22 + 11x + 6x2 = 0 Solving -22 + 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'. -3.666666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 1.833333333x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 1.833333333x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 1.833333333x + x2 = 0 + 3.666666667 1.833333333x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 1.833333333x + x2 = 3.666666667 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 = 3.666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 3.666666667 + 0.8402777775 Combine like terms: 3.666666667 + 0.8402777775 = 4.5069444445 0.8402777775 + 1.833333333x + x2 = 4.5069444445 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 4.5069444445 Calculate the square root of the right side: 2.122956534 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 2.122956534 and -2.122956534.Subproblem 1
x + 0.9166666665 = 2.122956534 Simplifying x + 0.9166666665 = 2.122956534 Reorder the terms: 0.9166666665 + x = 2.122956534 Solving 0.9166666665 + x = 2.122956534 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 = 2.122956534 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 2.122956534 + -0.9166666665 x = 2.122956534 + -0.9166666665 Combine like terms: 2.122956534 + -0.9166666665 = 1.2062898675 x = 1.2062898675 Simplifying x = 1.2062898675Subproblem 2
x + 0.9166666665 = -2.122956534 Simplifying x + 0.9166666665 = -2.122956534 Reorder the terms: 0.9166666665 + x = -2.122956534 Solving 0.9166666665 + x = -2.122956534 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 = -2.122956534 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -2.122956534 + -0.9166666665 x = -2.122956534 + -0.9166666665 Combine like terms: -2.122956534 + -0.9166666665 = -3.0396232005 x = -3.0396232005 Simplifying x = -3.0396232005Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2062898675, -3.0396232005}
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