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Simplifying -2x(6x + -11) = -7 Reorder the terms: -2x(-11 + 6x) = -7 (-11 * -2x + 6x * -2x) = -7 (22x + -12x2) = -7 Solving 22x + -12x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 22x + -12x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 22x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.5833333333 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -1.833333333x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -1.833333333x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -1.833333333x + x2 = 0 + 0.5833333333 -1.833333333x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -1.833333333x + x2 = 0.5833333333 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 = 0.5833333333 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 0.5833333333 + 0.8402777775 Combine like terms: 0.5833333333 + 0.8402777775 = 1.4236111108 0.8402777775 + -1.833333333x + x2 = 1.4236111108 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 1.4236111108 Calculate the square root of the right side: 1.193151755 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 1.193151755 and -1.193151755.Subproblem 1
x + -0.9166666665 = 1.193151755 Simplifying x + -0.9166666665 = 1.193151755 Reorder the terms: -0.9166666665 + x = 1.193151755 Solving -0.9166666665 + x = 1.193151755 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 = 1.193151755 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.193151755 + 0.9166666665 x = 1.193151755 + 0.9166666665 Combine like terms: 1.193151755 + 0.9166666665 = 2.1098184215 x = 2.1098184215 Simplifying x = 2.1098184215Subproblem 2
x + -0.9166666665 = -1.193151755 Simplifying x + -0.9166666665 = -1.193151755 Reorder the terms: -0.9166666665 + x = -1.193151755 Solving -0.9166666665 + x = -1.193151755 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 = -1.193151755 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.193151755 + 0.9166666665 x = -1.193151755 + 0.9166666665 Combine like terms: -1.193151755 + 0.9166666665 = -0.2764850885 x = -0.2764850885 Simplifying x = -0.2764850885Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1098184215, -0.2764850885}
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