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Simplifying 6x2 + 11x + -100 = 0 Reorder the terms: -100 + 11x + 6x2 = 0 Solving -100 + 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'. -16.66666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + 1.833333333x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + 1.833333333x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + 1.833333333x + x2 = 0 + 16.66666667 1.833333333x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 1.833333333x + x2 = 16.66666667 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 = 16.66666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 16.66666667 + 0.8402777775 Combine like terms: 16.66666667 + 0.8402777775 = 17.5069444475 0.8402777775 + 1.833333333x + x2 = 17.5069444475 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 17.5069444475 Calculate the square root of the right side: 4.184130071 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 4.184130071 and -4.184130071.Subproblem 1
x + 0.9166666665 = 4.184130071 Simplifying x + 0.9166666665 = 4.184130071 Reorder the terms: 0.9166666665 + x = 4.184130071 Solving 0.9166666665 + x = 4.184130071 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 = 4.184130071 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 4.184130071 + -0.9166666665 x = 4.184130071 + -0.9166666665 Combine like terms: 4.184130071 + -0.9166666665 = 3.2674634045 x = 3.2674634045 Simplifying x = 3.2674634045Subproblem 2
x + 0.9166666665 = -4.184130071 Simplifying x + 0.9166666665 = -4.184130071 Reorder the terms: 0.9166666665 + x = -4.184130071 Solving 0.9166666665 + x = -4.184130071 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 = -4.184130071 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -4.184130071 + -0.9166666665 x = -4.184130071 + -0.9166666665 Combine like terms: -4.184130071 + -0.9166666665 = -5.1007967375 x = -5.1007967375 Simplifying x = -5.1007967375Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2674634045, -5.1007967375}
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