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Simplifying -21x2 + 11x + 46 = 0 Reorder the terms: 46 + 11x + -21x2 = 0 Solving 46 + 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'. -2.19047619 + -0.5238095238x + x2 = 0 Move the constant term to the right: Add '2.19047619' to each side of the equation. -2.19047619 + -0.5238095238x + 2.19047619 + x2 = 0 + 2.19047619 Reorder the terms: -2.19047619 + 2.19047619 + -0.5238095238x + x2 = 0 + 2.19047619 Combine like terms: -2.19047619 + 2.19047619 = 0.00000000 0.00000000 + -0.5238095238x + x2 = 0 + 2.19047619 -0.5238095238x + x2 = 0 + 2.19047619 Combine like terms: 0 + 2.19047619 = 2.19047619 -0.5238095238x + x2 = 2.19047619 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 = 2.19047619 + 0.06859410431 Reorder the terms: 0.06859410431 + -0.5238095238x + x2 = 2.19047619 + 0.06859410431 Combine like terms: 2.19047619 + 0.06859410431 = 2.25907029431 0.06859410431 + -0.5238095238x + x2 = 2.25907029431 Factor a perfect square on the left side: (x + -0.2619047619)(x + -0.2619047619) = 2.25907029431 Calculate the square root of the right side: 1.503020391 Break this problem into two subproblems by setting (x + -0.2619047619) equal to 1.503020391 and -1.503020391.Subproblem 1
x + -0.2619047619 = 1.503020391 Simplifying x + -0.2619047619 = 1.503020391 Reorder the terms: -0.2619047619 + x = 1.503020391 Solving -0.2619047619 + x = 1.503020391 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 = 1.503020391 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + x = 1.503020391 + 0.2619047619 x = 1.503020391 + 0.2619047619 Combine like terms: 1.503020391 + 0.2619047619 = 1.7649251529 x = 1.7649251529 Simplifying x = 1.7649251529Subproblem 2
x + -0.2619047619 = -1.503020391 Simplifying x + -0.2619047619 = -1.503020391 Reorder the terms: -0.2619047619 + x = -1.503020391 Solving -0.2619047619 + x = -1.503020391 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 = -1.503020391 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + x = -1.503020391 + 0.2619047619 x = -1.503020391 + 0.2619047619 Combine like terms: -1.503020391 + 0.2619047619 = -1.2411156291 x = -1.2411156291 Simplifying x = -1.2411156291Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7649251529, -1.2411156291}
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