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Simplifying 17000 = x2 + -2x + 2 Reorder the terms: 17000 = 2 + -2x + x2 Solving 17000 = 2 + -2x + x2 Solving for variable 'x'. Combine like terms: 17000 + -2 = 16998 16998 + 2x + -1x2 = 2 + -2x + x2 + -2 + 2x + -1x2 Reorder the terms: 16998 + 2x + -1x2 = 2 + -2 + -2x + 2x + x2 + -1x2 Combine like terms: 2 + -2 = 0 16998 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 16998 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 16998 + 2x + -1x2 = 0 + x2 + -1x2 16998 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 16998 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16998 + -2x + x2 = 0 Move the constant term to the right: Add '16998' to each side of the equation. -16998 + -2x + 16998 + x2 = 0 + 16998 Reorder the terms: -16998 + 16998 + -2x + x2 = 0 + 16998 Combine like terms: -16998 + 16998 = 0 0 + -2x + x2 = 0 + 16998 -2x + x2 = 0 + 16998 Combine like terms: 0 + 16998 = 16998 -2x + x2 = 16998 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 = 16998 + 1 Reorder the terms: 1 + -2x + x2 = 16998 + 1 Combine like terms: 16998 + 1 = 16999 1 + -2x + x2 = 16999 Factor a perfect square on the left side: (x + -1)(x + -1) = 16999 Calculate the square root of the right side: 130.380213223 Break this problem into two subproblems by setting (x + -1) equal to 130.380213223 and -130.380213223.Subproblem 1
x + -1 = 130.380213223 Simplifying x + -1 = 130.380213223 Reorder the terms: -1 + x = 130.380213223 Solving -1 + x = 130.380213223 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 = 130.380213223 + 1 Combine like terms: -1 + 1 = 0 0 + x = 130.380213223 + 1 x = 130.380213223 + 1 Combine like terms: 130.380213223 + 1 = 131.380213223 x = 131.380213223 Simplifying x = 131.380213223Subproblem 2
x + -1 = -130.380213223 Simplifying x + -1 = -130.380213223 Reorder the terms: -1 + x = -130.380213223 Solving -1 + x = -130.380213223 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 = -130.380213223 + 1 Combine like terms: -1 + 1 = 0 0 + x = -130.380213223 + 1 x = -130.380213223 + 1 Combine like terms: -130.380213223 + 1 = -129.380213223 x = -129.380213223 Simplifying x = -129.380213223Solution
The solution to the problem is based on the solutions from the subproblems. x = {131.380213223, -129.380213223}
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