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Simplifying 21x2 + -11x + -21 = 0 Reorder the terms: -21 + -11x + 21x2 = 0 Solving -21 + -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'. -1 + -0.5238095238x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5238095238x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5238095238x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5238095238x + x2 = 0 + 1 -0.5238095238x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5238095238x + x2 = 1 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 = 1 + 0.06859410431 Reorder the terms: 0.06859410431 + -0.5238095238x + x2 = 1 + 0.06859410431 Combine like terms: 1 + 0.06859410431 = 1.06859410431 0.06859410431 + -0.5238095238x + x2 = 1.06859410431 Factor a perfect square on the left side: (x + -0.2619047619)(x + -0.2619047619) = 1.06859410431 Calculate the square root of the right side: 1.033728255 Break this problem into two subproblems by setting (x + -0.2619047619) equal to 1.033728255 and -1.033728255.Subproblem 1
x + -0.2619047619 = 1.033728255 Simplifying x + -0.2619047619 = 1.033728255 Reorder the terms: -0.2619047619 + x = 1.033728255 Solving -0.2619047619 + x = 1.033728255 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 = 1.033728255 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + x = 1.033728255 + 0.2619047619 x = 1.033728255 + 0.2619047619 Combine like terms: 1.033728255 + 0.2619047619 = 1.2956330169 x = 1.2956330169 Simplifying x = 1.2956330169Subproblem 2
x + -0.2619047619 = -1.033728255 Simplifying x + -0.2619047619 = -1.033728255 Reorder the terms: -0.2619047619 + x = -1.033728255 Solving -0.2619047619 + x = -1.033728255 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 = -1.033728255 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + x = -1.033728255 + 0.2619047619 x = -1.033728255 + 0.2619047619 Combine like terms: -1.033728255 + 0.2619047619 = -0.7718234931 x = -0.7718234931 Simplifying x = -0.7718234931Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2956330169, -0.7718234931}
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