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Simplifying 6x2 + -11x + -30 = 384 Reorder the terms: -30 + -11x + 6x2 = 384 Solving -30 + -11x + 6x2 = 384 Solving for variable 'x'. Reorder the terms: -30 + -384 + -11x + 6x2 = 384 + -384 Combine like terms: -30 + -384 = -414 -414 + -11x + 6x2 = 384 + -384 Combine like terms: 384 + -384 = 0 -414 + -11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -69 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '69' to each side of the equation. -69 + -1.833333333x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + -1.833333333x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + -1.833333333x + x2 = 0 + 69 -1.833333333x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 -1.833333333x + x2 = 69 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 = 69 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 69 + 0.8402777775 Combine like terms: 69 + 0.8402777775 = 69.8402777775 0.8402777775 + -1.833333333x + x2 = 69.8402777775 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 69.8402777775 Calculate the square root of the right side: 8.357049586 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 8.357049586 and -8.357049586.Subproblem 1
x + -0.9166666665 = 8.357049586 Simplifying x + -0.9166666665 = 8.357049586 Reorder the terms: -0.9166666665 + x = 8.357049586 Solving -0.9166666665 + x = 8.357049586 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 = 8.357049586 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 8.357049586 + 0.9166666665 x = 8.357049586 + 0.9166666665 Combine like terms: 8.357049586 + 0.9166666665 = 9.2737162525 x = 9.2737162525 Simplifying x = 9.2737162525Subproblem 2
x + -0.9166666665 = -8.357049586 Simplifying x + -0.9166666665 = -8.357049586 Reorder the terms: -0.9166666665 + x = -8.357049586 Solving -0.9166666665 + x = -8.357049586 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 = -8.357049586 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -8.357049586 + 0.9166666665 x = -8.357049586 + 0.9166666665 Combine like terms: -8.357049586 + 0.9166666665 = -7.4403829195 x = -7.4403829195 Simplifying x = -7.4403829195Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.2737162525, -7.4403829195}
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