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Simplifying x2 + 4x + -1007696 = 0 Reorder the terms: -1007696 + 4x + x2 = 0 Solving -1007696 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1007696' to each side of the equation. -1007696 + 4x + 1007696 + x2 = 0 + 1007696 Reorder the terms: -1007696 + 1007696 + 4x + x2 = 0 + 1007696 Combine like terms: -1007696 + 1007696 = 0 0 + 4x + x2 = 0 + 1007696 4x + x2 = 0 + 1007696 Combine like terms: 0 + 1007696 = 1007696 4x + x2 = 1007696 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1007696 + 4 Reorder the terms: 4 + 4x + x2 = 1007696 + 4 Combine like terms: 1007696 + 4 = 1007700 4 + 4x + x2 = 1007700 Factor a perfect square on the left side: (x + 2)(x + 2) = 1007700 Calculate the square root of the right side: 1003.842617147 Break this problem into two subproblems by setting (x + 2) equal to 1003.842617147 and -1003.842617147.Subproblem 1
x + 2 = 1003.842617147 Simplifying x + 2 = 1003.842617147 Reorder the terms: 2 + x = 1003.842617147 Solving 2 + x = 1003.842617147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1003.842617147 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1003.842617147 + -2 x = 1003.842617147 + -2 Combine like terms: 1003.842617147 + -2 = 1001.842617147 x = 1001.842617147 Simplifying x = 1001.842617147Subproblem 2
x + 2 = -1003.842617147 Simplifying x + 2 = -1003.842617147 Reorder the terms: 2 + x = -1003.842617147 Solving 2 + x = -1003.842617147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1003.842617147 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1003.842617147 + -2 x = -1003.842617147 + -2 Combine like terms: -1003.842617147 + -2 = -1005.842617147 x = -1005.842617147 Simplifying x = -1005.842617147Solution
The solution to the problem is based on the solutions from the subproblems. x = {1001.842617147, -1005.842617147}
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