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Simplifying x2 + -22x + 121 = 12 Reorder the terms: 121 + -22x + x2 = 12 Solving 121 + -22x + x2 = 12 Solving for variable 'x'. Reorder the terms: 121 + -12 + -22x + x2 = 12 + -12 Combine like terms: 121 + -12 = 109 109 + -22x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 109 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-109' to each side of the equation. 109 + -22x + -109 + x2 = 0 + -109 Reorder the terms: 109 + -109 + -22x + x2 = 0 + -109 Combine like terms: 109 + -109 = 0 0 + -22x + x2 = 0 + -109 -22x + x2 = 0 + -109 Combine like terms: 0 + -109 = -109 -22x + x2 = -109 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 = -109 + 121 Reorder the terms: 121 + -22x + x2 = -109 + 121 Combine like terms: -109 + 121 = 12 121 + -22x + x2 = 12 Factor a perfect square on the left side: (x + -11)(x + -11) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -11) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -11 = 3.464101615 Simplifying x + -11 = 3.464101615 Reorder the terms: -11 + x = 3.464101615 Solving -11 + x = 3.464101615 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 = 3.464101615 + 11 Combine like terms: -11 + 11 = 0 0 + x = 3.464101615 + 11 x = 3.464101615 + 11 Combine like terms: 3.464101615 + 11 = 14.464101615 x = 14.464101615 Simplifying x = 14.464101615Subproblem 2
x + -11 = -3.464101615 Simplifying x + -11 = -3.464101615 Reorder the terms: -11 + x = -3.464101615 Solving -11 + x = -3.464101615 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 = -3.464101615 + 11 Combine like terms: -11 + 11 = 0 0 + x = -3.464101615 + 11 x = -3.464101615 + 11 Combine like terms: -3.464101615 + 11 = 7.535898385 x = 7.535898385 Simplifying x = 7.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.464101615, 7.535898385}
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