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Simplifying x2 + -22x + 121 = 54 Reorder the terms: 121 + -22x + x2 = 54 Solving 121 + -22x + x2 = 54 Solving for variable 'x'. Reorder the terms: 121 + -54 + -22x + x2 = 54 + -54 Combine like terms: 121 + -54 = 67 67 + -22x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 67 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-67' to each side of the equation. 67 + -22x + -67 + x2 = 0 + -67 Reorder the terms: 67 + -67 + -22x + x2 = 0 + -67 Combine like terms: 67 + -67 = 0 0 + -22x + x2 = 0 + -67 -22x + x2 = 0 + -67 Combine like terms: 0 + -67 = -67 -22x + x2 = -67 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 = -67 + 121 Reorder the terms: 121 + -22x + x2 = -67 + 121 Combine like terms: -67 + 121 = 54 121 + -22x + x2 = 54 Factor a perfect square on the left side: (x + -11)(x + -11) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -11) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -11 = 7.348469228 Simplifying x + -11 = 7.348469228 Reorder the terms: -11 + x = 7.348469228 Solving -11 + x = 7.348469228 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 = 7.348469228 + 11 Combine like terms: -11 + 11 = 0 0 + x = 7.348469228 + 11 x = 7.348469228 + 11 Combine like terms: 7.348469228 + 11 = 18.348469228 x = 18.348469228 Simplifying x = 18.348469228Subproblem 2
x + -11 = -7.348469228 Simplifying x + -11 = -7.348469228 Reorder the terms: -11 + x = -7.348469228 Solving -11 + x = -7.348469228 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 = -7.348469228 + 11 Combine like terms: -11 + 11 = 0 0 + x = -7.348469228 + 11 x = -7.348469228 + 11 Combine like terms: -7.348469228 + 11 = 3.651530772 x = 3.651530772 Simplifying x = 3.651530772Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.348469228, 3.651530772}
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