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Simplifying 21x2 + -47x + -88 = 0 Reorder the terms: -88 + -47x + 21x2 = 0 Solving -88 + -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'. -4.19047619 + -2.238095238x + x2 = 0 Move the constant term to the right: Add '4.19047619' to each side of the equation. -4.19047619 + -2.238095238x + 4.19047619 + x2 = 0 + 4.19047619 Reorder the terms: -4.19047619 + 4.19047619 + -2.238095238x + x2 = 0 + 4.19047619 Combine like terms: -4.19047619 + 4.19047619 = 0.00000000 0.00000000 + -2.238095238x + x2 = 0 + 4.19047619 -2.238095238x + x2 = 0 + 4.19047619 Combine like terms: 0 + 4.19047619 = 4.19047619 -2.238095238x + x2 = 4.19047619 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 = 4.19047619 + 1.252267574 Reorder the terms: 1.252267574 + -2.238095238x + x2 = 4.19047619 + 1.252267574 Combine like terms: 4.19047619 + 1.252267574 = 5.442743764 1.252267574 + -2.238095238x + x2 = 5.442743764 Factor a perfect square on the left side: (x + -1.119047619)(x + -1.119047619) = 5.442743764 Calculate the square root of the right side: 2.332968873 Break this problem into two subproblems by setting (x + -1.119047619) equal to 2.332968873 and -2.332968873.Subproblem 1
x + -1.119047619 = 2.332968873 Simplifying x + -1.119047619 = 2.332968873 Reorder the terms: -1.119047619 + x = 2.332968873 Solving -1.119047619 + x = 2.332968873 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 = 2.332968873 + 1.119047619 Combine like terms: -1.119047619 + 1.119047619 = 0.000000000 0.000000000 + x = 2.332968873 + 1.119047619 x = 2.332968873 + 1.119047619 Combine like terms: 2.332968873 + 1.119047619 = 3.452016492 x = 3.452016492 Simplifying x = 3.452016492Subproblem 2
x + -1.119047619 = -2.332968873 Simplifying x + -1.119047619 = -2.332968873 Reorder the terms: -1.119047619 + x = -2.332968873 Solving -1.119047619 + x = -2.332968873 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 = -2.332968873 + 1.119047619 Combine like terms: -1.119047619 + 1.119047619 = 0.000000000 0.000000000 + x = -2.332968873 + 1.119047619 x = -2.332968873 + 1.119047619 Combine like terms: -2.332968873 + 1.119047619 = -1.213921254 x = -1.213921254 Simplifying x = -1.213921254Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.452016492, -1.213921254}
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