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Simplifying X2 + -2X + -1000 = 0 Reorder the terms: -1000 + -2X + X2 = 0 Solving -1000 + -2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -2X + 1000 + X2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -2X + X2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -2X + X2 = 0 + 1000 -2X + X2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -2X + X2 = 1000 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = 1000 + 1 Reorder the terms: 1 + -2X + X2 = 1000 + 1 Combine like terms: 1000 + 1 = 1001 1 + -2X + X2 = 1001 Factor a perfect square on the left side: (X + -1)(X + -1) = 1001 Calculate the square root of the right side: 31.638584039 Break this problem into two subproblems by setting (X + -1) equal to 31.638584039 and -31.638584039.Subproblem 1
X + -1 = 31.638584039 Simplifying X + -1 = 31.638584039 Reorder the terms: -1 + X = 31.638584039 Solving -1 + X = 31.638584039 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 31.638584039 + 1 Combine like terms: -1 + 1 = 0 0 + X = 31.638584039 + 1 X = 31.638584039 + 1 Combine like terms: 31.638584039 + 1 = 32.638584039 X = 32.638584039 Simplifying X = 32.638584039Subproblem 2
X + -1 = -31.638584039 Simplifying X + -1 = -31.638584039 Reorder the terms: -1 + X = -31.638584039 Solving -1 + X = -31.638584039 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -31.638584039 + 1 Combine like terms: -1 + 1 = 0 0 + X = -31.638584039 + 1 X = -31.638584039 + 1 Combine like terms: -31.638584039 + 1 = -30.638584039 X = -30.638584039 Simplifying X = -30.638584039Solution
The solution to the problem is based on the solutions from the subproblems. X = {32.638584039, -30.638584039}
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