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Simplifying x2 + -22x + -73 = 0 Reorder the terms: -73 + -22x + x2 = 0 Solving -73 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -22x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + -22x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -22x + x2 = 0 + 73 -22x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 -22x + x2 = 73 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 = 73 + 121 Reorder the terms: 121 + -22x + x2 = 73 + 121 Combine like terms: 73 + 121 = 194 121 + -22x + x2 = 194 Factor a perfect square on the left side: (x + -11)(x + -11) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (x + -11) equal to 13.928388277 and -13.928388277.Subproblem 1
x + -11 = 13.928388277 Simplifying x + -11 = 13.928388277 Reorder the terms: -11 + x = 13.928388277 Solving -11 + x = 13.928388277 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 = 13.928388277 + 11 Combine like terms: -11 + 11 = 0 0 + x = 13.928388277 + 11 x = 13.928388277 + 11 Combine like terms: 13.928388277 + 11 = 24.928388277 x = 24.928388277 Simplifying x = 24.928388277Subproblem 2
x + -11 = -13.928388277 Simplifying x + -11 = -13.928388277 Reorder the terms: -11 + x = -13.928388277 Solving -11 + x = -13.928388277 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 = -13.928388277 + 11 Combine like terms: -11 + 11 = 0 0 + x = -13.928388277 + 11 x = -13.928388277 + 11 Combine like terms: -13.928388277 + 11 = -2.928388277 x = -2.928388277 Simplifying x = -2.928388277Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.928388277, -2.928388277}
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