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Simplifying x2 + -210x + -2000 = 0 Reorder the terms: -2000 + -210x + x2 = 0 Solving -2000 + -210x + 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 + -210x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -210x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -210x + x2 = 0 + 2000 -210x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -210x + x2 = 2000 The x term is -210x. Take half its coefficient (-105). Square it (11025) and add it to both sides. Add '11025' to each side of the equation. -210x + 11025 + x2 = 2000 + 11025 Reorder the terms: 11025 + -210x + x2 = 2000 + 11025 Combine like terms: 2000 + 11025 = 13025 11025 + -210x + x2 = 13025 Factor a perfect square on the left side: (x + -105)(x + -105) = 13025 Calculate the square root of the right side: 114.127122105 Break this problem into two subproblems by setting (x + -105) equal to 114.127122105 and -114.127122105.Subproblem 1
x + -105 = 114.127122105 Simplifying x + -105 = 114.127122105 Reorder the terms: -105 + x = 114.127122105 Solving -105 + x = 114.127122105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x = 114.127122105 + 105 Combine like terms: -105 + 105 = 0 0 + x = 114.127122105 + 105 x = 114.127122105 + 105 Combine like terms: 114.127122105 + 105 = 219.127122105 x = 219.127122105 Simplifying x = 219.127122105Subproblem 2
x + -105 = -114.127122105 Simplifying x + -105 = -114.127122105 Reorder the terms: -105 + x = -114.127122105 Solving -105 + x = -114.127122105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x = -114.127122105 + 105 Combine like terms: -105 + 105 = 0 0 + x = -114.127122105 + 105 x = -114.127122105 + 105 Combine like terms: -114.127122105 + 105 = -9.127122105 x = -9.127122105 Simplifying x = -9.127122105Solution
The solution to the problem is based on the solutions from the subproblems. x = {219.127122105, -9.127122105}
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