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Simplifying x2 + -220x + 11000 = 0 Reorder the terms: 11000 + -220x + x2 = 0 Solving 11000 + -220x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11000' to each side of the equation. 11000 + -220x + -11000 + x2 = 0 + -11000 Reorder the terms: 11000 + -11000 + -220x + x2 = 0 + -11000 Combine like terms: 11000 + -11000 = 0 0 + -220x + x2 = 0 + -11000 -220x + x2 = 0 + -11000 Combine like terms: 0 + -11000 = -11000 -220x + x2 = -11000 The x term is -220x. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220x + 12100 + x2 = -11000 + 12100 Reorder the terms: 12100 + -220x + x2 = -11000 + 12100 Combine like terms: -11000 + 12100 = 1100 12100 + -220x + x2 = 1100 Factor a perfect square on the left side: (x + -110)(x + -110) = 1100 Calculate the square root of the right side: 33.166247904 Break this problem into two subproblems by setting (x + -110) equal to 33.166247904 and -33.166247904.Subproblem 1
x + -110 = 33.166247904 Simplifying x + -110 = 33.166247904 Reorder the terms: -110 + x = 33.166247904 Solving -110 + x = 33.166247904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 33.166247904 + 110 Combine like terms: -110 + 110 = 0 0 + x = 33.166247904 + 110 x = 33.166247904 + 110 Combine like terms: 33.166247904 + 110 = 143.166247904 x = 143.166247904 Simplifying x = 143.166247904Subproblem 2
x + -110 = -33.166247904 Simplifying x + -110 = -33.166247904 Reorder the terms: -110 + x = -33.166247904 Solving -110 + x = -33.166247904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -33.166247904 + 110 Combine like terms: -110 + 110 = 0 0 + x = -33.166247904 + 110 x = -33.166247904 + 110 Combine like terms: -33.166247904 + 110 = 76.833752096 x = 76.833752096 Simplifying x = 76.833752096Solution
The solution to the problem is based on the solutions from the subproblems. x = {143.166247904, 76.833752096}
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