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Simplifying x2 + -22x + 121 = 224 Reorder the terms: 121 + -22x + x2 = 224 Solving 121 + -22x + x2 = 224 Solving for variable 'x'. Reorder the terms: 121 + -224 + -22x + x2 = 224 + -224 Combine like terms: 121 + -224 = -103 -103 + -22x + x2 = 224 + -224 Combine like terms: 224 + -224 = 0 -103 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '103' to each side of the equation. -103 + -22x + 103 + x2 = 0 + 103 Reorder the terms: -103 + 103 + -22x + x2 = 0 + 103 Combine like terms: -103 + 103 = 0 0 + -22x + x2 = 0 + 103 -22x + x2 = 0 + 103 Combine like terms: 0 + 103 = 103 -22x + x2 = 103 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 = 103 + 121 Reorder the terms: 121 + -22x + x2 = 103 + 121 Combine like terms: 103 + 121 = 224 121 + -22x + x2 = 224 Factor a perfect square on the left side: (x + -11)(x + -11) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x + -11) equal to 14.966629547 and -14.966629547.Subproblem 1
x + -11 = 14.966629547 Simplifying x + -11 = 14.966629547 Reorder the terms: -11 + x = 14.966629547 Solving -11 + x = 14.966629547 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 = 14.966629547 + 11 Combine like terms: -11 + 11 = 0 0 + x = 14.966629547 + 11 x = 14.966629547 + 11 Combine like terms: 14.966629547 + 11 = 25.966629547 x = 25.966629547 Simplifying x = 25.966629547Subproblem 2
x + -11 = -14.966629547 Simplifying x + -11 = -14.966629547 Reorder the terms: -11 + x = -14.966629547 Solving -11 + x = -14.966629547 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 = -14.966629547 + 11 Combine like terms: -11 + 11 = 0 0 + x = -14.966629547 + 11 x = -14.966629547 + 11 Combine like terms: -14.966629547 + 11 = -3.966629547 x = -3.966629547 Simplifying x = -3.966629547Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.966629547, -3.966629547}
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