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Simplifying x2 + -22x + 121 = 125 Reorder the terms: 121 + -22x + x2 = 125 Solving 121 + -22x + x2 = 125 Solving for variable 'x'. Reorder the terms: 121 + -125 + -22x + x2 = 125 + -125 Combine like terms: 121 + -125 = -4 -4 + -22x + x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -4 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -22x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -22x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -22x + x2 = 0 + 4 -22x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -22x + x2 = 4 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 = 4 + 121 Reorder the terms: 121 + -22x + x2 = 4 + 121 Combine like terms: 4 + 121 = 125 121 + -22x + x2 = 125 Factor a perfect square on the left side: (x + -11)(x + -11) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -11) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -11 = 11.180339887 Simplifying x + -11 = 11.180339887 Reorder the terms: -11 + x = 11.180339887 Solving -11 + x = 11.180339887 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 = 11.180339887 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.180339887 + 11 x = 11.180339887 + 11 Combine like terms: 11.180339887 + 11 = 22.180339887 x = 22.180339887 Simplifying x = 22.180339887Subproblem 2
x + -11 = -11.180339887 Simplifying x + -11 = -11.180339887 Reorder the terms: -11 + x = -11.180339887 Solving -11 + x = -11.180339887 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 = -11.180339887 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.180339887 + 11 x = -11.180339887 + 11 Combine like terms: -11.180339887 + 11 = -0.180339887 x = -0.180339887 Simplifying x = -0.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.180339887, -0.180339887}
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