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Simplifying x2 + -22x + 121 = 255 Reorder the terms: 121 + -22x + x2 = 255 Solving 121 + -22x + x2 = 255 Solving for variable 'x'. Reorder the terms: 121 + -255 + -22x + x2 = 255 + -255 Combine like terms: 121 + -255 = -134 -134 + -22x + x2 = 255 + -255 Combine like terms: 255 + -255 = 0 -134 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '134' to each side of the equation. -134 + -22x + 134 + x2 = 0 + 134 Reorder the terms: -134 + 134 + -22x + x2 = 0 + 134 Combine like terms: -134 + 134 = 0 0 + -22x + x2 = 0 + 134 -22x + x2 = 0 + 134 Combine like terms: 0 + 134 = 134 -22x + x2 = 134 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 = 134 + 121 Reorder the terms: 121 + -22x + x2 = 134 + 121 Combine like terms: 134 + 121 = 255 121 + -22x + x2 = 255 Factor a perfect square on the left side: (x + -11)(x + -11) = 255 Calculate the square root of the right side: 15.968719423 Break this problem into two subproblems by setting (x + -11) equal to 15.968719423 and -15.968719423.Subproblem 1
x + -11 = 15.968719423 Simplifying x + -11 = 15.968719423 Reorder the terms: -11 + x = 15.968719423 Solving -11 + x = 15.968719423 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 = 15.968719423 + 11 Combine like terms: -11 + 11 = 0 0 + x = 15.968719423 + 11 x = 15.968719423 + 11 Combine like terms: 15.968719423 + 11 = 26.968719423 x = 26.968719423 Simplifying x = 26.968719423Subproblem 2
x + -11 = -15.968719423 Simplifying x + -11 = -15.968719423 Reorder the terms: -11 + x = -15.968719423 Solving -11 + x = -15.968719423 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 = -15.968719423 + 11 Combine like terms: -11 + 11 = 0 0 + x = -15.968719423 + 11 x = -15.968719423 + 11 Combine like terms: -15.968719423 + 11 = -4.968719423 x = -4.968719423 Simplifying x = -4.968719423Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.968719423, -4.968719423}
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