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Simplifying x2 + -22x + 2 = 0 Reorder the terms: 2 + -22x + x2 = 0 Solving 2 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -22x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -22x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -22x + x2 = 0 + -2 -22x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -22x + x2 = -2 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -2 + 121 Reorder the terms: 121 + -22x + x2 = -2 + 121 Combine like terms: -2 + 121 = 119 121 + -22x + x2 = 119 Factor a perfect square on the left side: (x + -11)(x + -11) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + -11) equal to 10.908712115 and -10.908712115.Subproblem 1
x + -11 = 10.908712115 Simplifying x + -11 = 10.908712115 Reorder the terms: -11 + x = 10.908712115 Solving -11 + x = 10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 10.908712115 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.908712115 + 11 x = 10.908712115 + 11 Combine like terms: 10.908712115 + 11 = 21.908712115 x = 21.908712115 Simplifying x = 21.908712115Subproblem 2
x + -11 = -10.908712115 Simplifying x + -11 = -10.908712115 Reorder the terms: -11 + x = -10.908712115 Solving -11 + x = -10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -10.908712115 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.908712115 + 11 x = -10.908712115 + 11 Combine like terms: -10.908712115 + 11 = 0.091287885 x = 0.091287885 Simplifying x = 0.091287885Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.908712115, 0.091287885}
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