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Simplifying 7000 = x2 + -1x + 1 Reorder the terms: 7000 = 1 + -1x + x2 Solving 7000 = 1 + -1x + x2 Solving for variable 'x'. Combine like terms: 7000 + -1 = 6999 6999 + x + -1x2 = 1 + -1x + x2 + -1 + x + -1x2 Reorder the terms: 6999 + x + -1x2 = 1 + -1 + -1x + x + x2 + -1x2 Combine like terms: 1 + -1 = 0 6999 + x + -1x2 = 0 + -1x + x + x2 + -1x2 6999 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 6999 + x + -1x2 = 0 + x2 + -1x2 6999 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6999 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6999 + -1x + x2 = 0 Move the constant term to the right: Add '6999' to each side of the equation. -6999 + -1x + 6999 + x2 = 0 + 6999 Reorder the terms: -6999 + 6999 + -1x + x2 = 0 + 6999 Combine like terms: -6999 + 6999 = 0 0 + -1x + x2 = 0 + 6999 -1x + x2 = 0 + 6999 Combine like terms: 0 + 6999 = 6999 -1x + x2 = 6999 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 6999 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6999 + 0.25 Combine like terms: 6999 + 0.25 = 6999.25 0.25 + -1x + x2 = 6999.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6999.25 Calculate the square root of the right side: 83.661520426 Break this problem into two subproblems by setting (x + 0.5) equal to 83.661520426 and -83.661520426.Subproblem 1
x + 0.5 = 83.661520426 Simplifying x + 0.5 = 83.661520426 Reorder the terms: 0.5 + x = 83.661520426 Solving 0.5 + x = 83.661520426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 83.661520426 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 83.661520426 + -0.5 x = 83.661520426 + -0.5 Combine like terms: 83.661520426 + -0.5 = 83.161520426 x = 83.161520426 Simplifying x = 83.161520426Subproblem 2
x + 0.5 = -83.661520426 Simplifying x + 0.5 = -83.661520426 Reorder the terms: 0.5 + x = -83.661520426 Solving 0.5 + x = -83.661520426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -83.661520426 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -83.661520426 + -0.5 x = -83.661520426 + -0.5 Combine like terms: -83.661520426 + -0.5 = -84.161520426 x = -84.161520426 Simplifying x = -84.161520426Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.161520426, -84.161520426}
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