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Simplifying 21x2 + -47x + -64 = 0 Reorder the terms: -64 + -47x + 21x2 = 0 Solving -64 + -47x + 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'. -3.047619048 + -2.238095238x + x2 = 0 Move the constant term to the right: Add '3.047619048' to each side of the equation. -3.047619048 + -2.238095238x + 3.047619048 + x2 = 0 + 3.047619048 Reorder the terms: -3.047619048 + 3.047619048 + -2.238095238x + x2 = 0 + 3.047619048 Combine like terms: -3.047619048 + 3.047619048 = 0.000000000 0.000000000 + -2.238095238x + x2 = 0 + 3.047619048 -2.238095238x + x2 = 0 + 3.047619048 Combine like terms: 0 + 3.047619048 = 3.047619048 -2.238095238x + x2 = 3.047619048 The x term is -2.238095238x. Take half its coefficient (-1.119047619). Square it (1.252267574) and add it to both sides. Add '1.252267574' to each side of the equation. -2.238095238x + 1.252267574 + x2 = 3.047619048 + 1.252267574 Reorder the terms: 1.252267574 + -2.238095238x + x2 = 3.047619048 + 1.252267574 Combine like terms: 3.047619048 + 1.252267574 = 4.299886622 1.252267574 + -2.238095238x + x2 = 4.299886622 Factor a perfect square on the left side: (x + -1.119047619)(x + -1.119047619) = 4.299886622 Calculate the square root of the right side: 2.073616797 Break this problem into two subproblems by setting (x + -1.119047619) equal to 2.073616797 and -2.073616797.Subproblem 1
x + -1.119047619 = 2.073616797 Simplifying x + -1.119047619 = 2.073616797 Reorder the terms: -1.119047619 + x = 2.073616797 Solving -1.119047619 + x = 2.073616797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.119047619' to each side of the equation. -1.119047619 + 1.119047619 + x = 2.073616797 + 1.119047619 Combine like terms: -1.119047619 + 1.119047619 = 0.000000000 0.000000000 + x = 2.073616797 + 1.119047619 x = 2.073616797 + 1.119047619 Combine like terms: 2.073616797 + 1.119047619 = 3.192664416 x = 3.192664416 Simplifying x = 3.192664416Subproblem 2
x + -1.119047619 = -2.073616797 Simplifying x + -1.119047619 = -2.073616797 Reorder the terms: -1.119047619 + x = -2.073616797 Solving -1.119047619 + x = -2.073616797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.119047619' to each side of the equation. -1.119047619 + 1.119047619 + x = -2.073616797 + 1.119047619 Combine like terms: -1.119047619 + 1.119047619 = 0.000000000 0.000000000 + x = -2.073616797 + 1.119047619 x = -2.073616797 + 1.119047619 Combine like terms: -2.073616797 + 1.119047619 = -0.954569178 x = -0.954569178 Simplifying x = -0.954569178Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.192664416, -0.954569178}
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