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Simplifying 21x2 + -11x + 1 = 0 Reorder the terms: 1 + -11x + 21x2 = 0 Solving 1 + -11x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.04761904762 + -0.5238095238x + x2 = 0 Move the constant term to the right: Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.5238095238x + -0.04761904762 + x2 = 0 + -0.04761904762 Reorder the terms: 0.04761904762 + -0.04761904762 + -0.5238095238x + x2 = 0 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + -0.5238095238x + x2 = 0 + -0.04761904762 -0.5238095238x + x2 = 0 + -0.04761904762 Combine like terms: 0 + -0.04761904762 = -0.04761904762 -0.5238095238x + x2 = -0.04761904762 The x term is -0.5238095238x. Take half its coefficient (-0.2619047619). Square it (0.06859410431) and add it to both sides. Add '0.06859410431' to each side of the equation. -0.5238095238x + 0.06859410431 + x2 = -0.04761904762 + 0.06859410431 Reorder the terms: 0.06859410431 + -0.5238095238x + x2 = -0.04761904762 + 0.06859410431 Combine like terms: -0.04761904762 + 0.06859410431 = 0.02097505669 0.06859410431 + -0.5238095238x + x2 = 0.02097505669 Factor a perfect square on the left side: (x + -0.2619047619)(x + -0.2619047619) = 0.02097505669 Calculate the square root of the right side: 0.144827679 Break this problem into two subproblems by setting (x + -0.2619047619) equal to 0.144827679 and -0.144827679.Subproblem 1
x + -0.2619047619 = 0.144827679 Simplifying x + -0.2619047619 = 0.144827679 Reorder the terms: -0.2619047619 + x = 0.144827679 Solving -0.2619047619 + x = 0.144827679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2619047619' to each side of the equation. -0.2619047619 + 0.2619047619 + x = 0.144827679 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + x = 0.144827679 + 0.2619047619 x = 0.144827679 + 0.2619047619 Combine like terms: 0.144827679 + 0.2619047619 = 0.4067324409 x = 0.4067324409 Simplifying x = 0.4067324409Subproblem 2
x + -0.2619047619 = -0.144827679 Simplifying x + -0.2619047619 = -0.144827679 Reorder the terms: -0.2619047619 + x = -0.144827679 Solving -0.2619047619 + x = -0.144827679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2619047619' to each side of the equation. -0.2619047619 + 0.2619047619 + x = -0.144827679 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + x = -0.144827679 + 0.2619047619 x = -0.144827679 + 0.2619047619 Combine like terms: -0.144827679 + 0.2619047619 = 0.1170770829 x = 0.1170770829 Simplifying x = 0.1170770829Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4067324409, 0.1170770829}
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