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Simplifying x2 + -120 * 11x + 121 * 11 = 0 Multiply -120 * 11 x2 + -1320x + 121 * 11 = 0 Multiply 121 * 11 x2 + -1320x + 1331 = 0 Reorder the terms: 1331 + -1320x + x2 = 0 Solving 1331 + -1320x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1331' to each side of the equation. 1331 + -1320x + -1331 + x2 = 0 + -1331 Reorder the terms: 1331 + -1331 + -1320x + x2 = 0 + -1331 Combine like terms: 1331 + -1331 = 0 0 + -1320x + x2 = 0 + -1331 -1320x + x2 = 0 + -1331 Combine like terms: 0 + -1331 = -1331 -1320x + x2 = -1331 The x term is -1320x. Take half its coefficient (-660). Square it (435600) and add it to both sides. Add '435600' to each side of the equation. -1320x + 435600 + x2 = -1331 + 435600 Reorder the terms: 435600 + -1320x + x2 = -1331 + 435600 Combine like terms: -1331 + 435600 = 434269 435600 + -1320x + x2 = 434269 Factor a perfect square on the left side: (x + -660)(x + -660) = 434269 Calculate the square root of the right side: 658.990895233 Break this problem into two subproblems by setting (x + -660) equal to 658.990895233 and -658.990895233.Subproblem 1
x + -660 = 658.990895233 Simplifying x + -660 = 658.990895233 Reorder the terms: -660 + x = 658.990895233 Solving -660 + x = 658.990895233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '660' to each side of the equation. -660 + 660 + x = 658.990895233 + 660 Combine like terms: -660 + 660 = 0 0 + x = 658.990895233 + 660 x = 658.990895233 + 660 Combine like terms: 658.990895233 + 660 = 1318.990895233 x = 1318.990895233 Simplifying x = 1318.990895233Subproblem 2
x + -660 = -658.990895233 Simplifying x + -660 = -658.990895233 Reorder the terms: -660 + x = -658.990895233 Solving -660 + x = -658.990895233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '660' to each side of the equation. -660 + 660 + x = -658.990895233 + 660 Combine like terms: -660 + 660 = 0 0 + x = -658.990895233 + 660 x = -658.990895233 + 660 Combine like terms: -658.990895233 + 660 = 1.009104767 x = 1.009104767 Simplifying x = 1.009104767Solution
The solution to the problem is based on the solutions from the subproblems. x = {1318.990895233, 1.009104767}
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