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Simplifying x2 + -22x + 110 = 0 Reorder the terms: 110 + -22x + x2 = 0 Solving 110 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-110' to each side of the equation. 110 + -22x + -110 + x2 = 0 + -110 Reorder the terms: 110 + -110 + -22x + x2 = 0 + -110 Combine like terms: 110 + -110 = 0 0 + -22x + x2 = 0 + -110 -22x + x2 = 0 + -110 Combine like terms: 0 + -110 = -110 -22x + x2 = -110 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 = -110 + 121 Reorder the terms: 121 + -22x + x2 = -110 + 121 Combine like terms: -110 + 121 = 11 121 + -22x + x2 = 11 Factor a perfect square on the left side: (x + -11)(x + -11) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -11) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -11 = 3.31662479 Simplifying x + -11 = 3.31662479 Reorder the terms: -11 + x = 3.31662479 Solving -11 + x = 3.31662479 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 = 3.31662479 + 11 Combine like terms: -11 + 11 = 0 0 + x = 3.31662479 + 11 x = 3.31662479 + 11 Combine like terms: 3.31662479 + 11 = 14.31662479 x = 14.31662479 Simplifying x = 14.31662479Subproblem 2
x + -11 = -3.31662479 Simplifying x + -11 = -3.31662479 Reorder the terms: -11 + x = -3.31662479 Solving -11 + x = -3.31662479 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 = -3.31662479 + 11 Combine like terms: -11 + 11 = 0 0 + x = -3.31662479 + 11 x = -3.31662479 + 11 Combine like terms: -3.31662479 + 11 = 7.68337521 x = 7.68337521 Simplifying x = 7.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.31662479, 7.68337521}
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