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Simplifying 21x2 + -23x + -6 = 0 Reorder the terms: -6 + -23x + 21x2 = 0 Solving -6 + -23x + 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'. -0.2857142857 + -1.095238095x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -1.095238095x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -1.095238095x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -1.095238095x + x2 = 0 + 0.2857142857 -1.095238095x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -1.095238095x + x2 = 0.2857142857 The x term is -1.095238095x. Take half its coefficient (-0.5476190475). Square it (0.2998866212) and add it to both sides. Add '0.2998866212' to each side of the equation. -1.095238095x + 0.2998866212 + x2 = 0.2857142857 + 0.2998866212 Reorder the terms: 0.2998866212 + -1.095238095x + x2 = 0.2857142857 + 0.2998866212 Combine like terms: 0.2857142857 + 0.2998866212 = 0.5856009069 0.2998866212 + -1.095238095x + x2 = 0.5856009069 Factor a perfect square on the left side: (x + -0.5476190475)(x + -0.5476190475) = 0.5856009069 Calculate the square root of the right side: 0.765245651 Break this problem into two subproblems by setting (x + -0.5476190475) equal to 0.765245651 and -0.765245651.Subproblem 1
x + -0.5476190475 = 0.765245651 Simplifying x + -0.5476190475 = 0.765245651 Reorder the terms: -0.5476190475 + x = 0.765245651 Solving -0.5476190475 + x = 0.765245651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5476190475' to each side of the equation. -0.5476190475 + 0.5476190475 + x = 0.765245651 + 0.5476190475 Combine like terms: -0.5476190475 + 0.5476190475 = 0.0000000000 0.0000000000 + x = 0.765245651 + 0.5476190475 x = 0.765245651 + 0.5476190475 Combine like terms: 0.765245651 + 0.5476190475 = 1.3128646985 x = 1.3128646985 Simplifying x = 1.3128646985Subproblem 2
x + -0.5476190475 = -0.765245651 Simplifying x + -0.5476190475 = -0.765245651 Reorder the terms: -0.5476190475 + x = -0.765245651 Solving -0.5476190475 + x = -0.765245651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5476190475' to each side of the equation. -0.5476190475 + 0.5476190475 + x = -0.765245651 + 0.5476190475 Combine like terms: -0.5476190475 + 0.5476190475 = 0.0000000000 0.0000000000 + x = -0.765245651 + 0.5476190475 x = -0.765245651 + 0.5476190475 Combine like terms: -0.765245651 + 0.5476190475 = -0.2176266035 x = -0.2176266035 Simplifying x = -0.2176266035Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3128646985, -0.2176266035}
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