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Simplifying 21x2 + -47x + -120 = 0 Reorder the terms: -120 + -47x + 21x2 = 0 Solving -120 + -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'. -5.714285714 + -2.238095238x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + -2.238095238x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + -2.238095238x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + -2.238095238x + x2 = 0 + 5.714285714 -2.238095238x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 -2.238095238x + x2 = 5.714285714 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 = 5.714285714 + 1.252267574 Reorder the terms: 1.252267574 + -2.238095238x + x2 = 5.714285714 + 1.252267574 Combine like terms: 5.714285714 + 1.252267574 = 6.966553288 1.252267574 + -2.238095238x + x2 = 6.966553288 Factor a perfect square on the left side: (x + -1.119047619)(x + -1.119047619) = 6.966553288 Calculate the square root of the right side: 2.639422908 Break this problem into two subproblems by setting (x + -1.119047619) equal to 2.639422908 and -2.639422908.Subproblem 1
x + -1.119047619 = 2.639422908 Simplifying x + -1.119047619 = 2.639422908 Reorder the terms: -1.119047619 + x = 2.639422908 Solving -1.119047619 + x = 2.639422908 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 = 2.639422908 + 1.119047619 Combine like terms: -1.119047619 + 1.119047619 = 0.000000000 0.000000000 + x = 2.639422908 + 1.119047619 x = 2.639422908 + 1.119047619 Combine like terms: 2.639422908 + 1.119047619 = 3.758470527 x = 3.758470527 Simplifying x = 3.758470527Subproblem 2
x + -1.119047619 = -2.639422908 Simplifying x + -1.119047619 = -2.639422908 Reorder the terms: -1.119047619 + x = -2.639422908 Solving -1.119047619 + x = -2.639422908 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 = -2.639422908 + 1.119047619 Combine like terms: -1.119047619 + 1.119047619 = 0.000000000 0.000000000 + x = -2.639422908 + 1.119047619 x = -2.639422908 + 1.119047619 Combine like terms: -2.639422908 + 1.119047619 = -1.520375289 x = -1.520375289 Simplifying x = -1.520375289Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.758470527, -1.520375289}
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