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Simplifying x2 + -22x + 60 = 0 Reorder the terms: 60 + -22x + x2 = 0 Solving 60 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -22x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -22x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -22x + x2 = 0 + -60 -22x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -22x + x2 = -60 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 = -60 + 121 Reorder the terms: 121 + -22x + x2 = -60 + 121 Combine like terms: -60 + 121 = 61 121 + -22x + x2 = 61 Factor a perfect square on the left side: (x + -11)(x + -11) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -11) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -11 = 7.810249676 Simplifying x + -11 = 7.810249676 Reorder the terms: -11 + x = 7.810249676 Solving -11 + x = 7.810249676 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 = 7.810249676 + 11 Combine like terms: -11 + 11 = 0 0 + x = 7.810249676 + 11 x = 7.810249676 + 11 Combine like terms: 7.810249676 + 11 = 18.810249676 x = 18.810249676 Simplifying x = 18.810249676Subproblem 2
x + -11 = -7.810249676 Simplifying x + -11 = -7.810249676 Reorder the terms: -11 + x = -7.810249676 Solving -11 + x = -7.810249676 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 = -7.810249676 + 11 Combine like terms: -11 + 11 = 0 0 + x = -7.810249676 + 11 x = -7.810249676 + 11 Combine like terms: -7.810249676 + 11 = 3.189750324 x = 3.189750324 Simplifying x = 3.189750324Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.810249676, 3.189750324}
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