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Simplifying x2 + -2x + -8999 = 0 Reorder the terms: -8999 + -2x + x2 = 0 Solving -8999 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8999' to each side of the equation. -8999 + -2x + 8999 + x2 = 0 + 8999 Reorder the terms: -8999 + 8999 + -2x + x2 = 0 + 8999 Combine like terms: -8999 + 8999 = 0 0 + -2x + x2 = 0 + 8999 -2x + x2 = 0 + 8999 Combine like terms: 0 + 8999 = 8999 -2x + x2 = 8999 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 = 8999 + 1 Reorder the terms: 1 + -2x + x2 = 8999 + 1 Combine like terms: 8999 + 1 = 9000 1 + -2x + x2 = 9000 Factor a perfect square on the left side: (x + -1)(x + -1) = 9000 Calculate the square root of the right side: 94.868329805 Break this problem into two subproblems by setting (x + -1) equal to 94.868329805 and -94.868329805.Subproblem 1
x + -1 = 94.868329805 Simplifying x + -1 = 94.868329805 Reorder the terms: -1 + x = 94.868329805 Solving -1 + x = 94.868329805 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 = 94.868329805 + 1 Combine like terms: -1 + 1 = 0 0 + x = 94.868329805 + 1 x = 94.868329805 + 1 Combine like terms: 94.868329805 + 1 = 95.868329805 x = 95.868329805 Simplifying x = 95.868329805Subproblem 2
x + -1 = -94.868329805 Simplifying x + -1 = -94.868329805 Reorder the terms: -1 + x = -94.868329805 Solving -1 + x = -94.868329805 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 = -94.868329805 + 1 Combine like terms: -1 + 1 = 0 0 + x = -94.868329805 + 1 x = -94.868329805 + 1 Combine like terms: -94.868329805 + 1 = -93.868329805 x = -93.868329805 Simplifying x = -93.868329805Solution
The solution to the problem is based on the solutions from the subproblems. x = {95.868329805, -93.868329805}
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