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Simplifying x2 + 2x = 1000 Reorder the terms: 2x + x2 = 1000 Solving 2x + x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 2x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 2x + x2 = 0 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 = 30.638584039 x = 30.638584039 Simplifying x = 30.638584039Subproblem 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 = -32.638584039 x = -32.638584039 Simplifying x = -32.638584039Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.638584039, -32.638584039}
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