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Simplifying x2 + -220x + 2000 = 0 Reorder the terms: 2000 + -220x + x2 = 0 Solving 2000 + -220x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + -220x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + -220x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -220x + x2 = 0 + -2000 -220x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -220x + x2 = -2000 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 = -2000 + 12100 Reorder the terms: 12100 + -220x + x2 = -2000 + 12100 Combine like terms: -2000 + 12100 = 10100 12100 + -220x + x2 = 10100 Factor a perfect square on the left side: (x + -110)(x + -110) = 10100 Calculate the square root of the right side: 100.498756211 Break this problem into two subproblems by setting (x + -110) equal to 100.498756211 and -100.498756211.Subproblem 1
x + -110 = 100.498756211 Simplifying x + -110 = 100.498756211 Reorder the terms: -110 + x = 100.498756211 Solving -110 + x = 100.498756211 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 = 100.498756211 + 110 Combine like terms: -110 + 110 = 0 0 + x = 100.498756211 + 110 x = 100.498756211 + 110 Combine like terms: 100.498756211 + 110 = 210.498756211 x = 210.498756211 Simplifying x = 210.498756211Subproblem 2
x + -110 = -100.498756211 Simplifying x + -110 = -100.498756211 Reorder the terms: -110 + x = -100.498756211 Solving -110 + x = -100.498756211 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 = -100.498756211 + 110 Combine like terms: -110 + 110 = 0 0 + x = -100.498756211 + 110 x = -100.498756211 + 110 Combine like terms: -100.498756211 + 110 = 9.501243789 x = 9.501243789 Simplifying x = 9.501243789Solution
The solution to the problem is based on the solutions from the subproblems. x = {210.498756211, 9.501243789}
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