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Simplifying 7000 = x2 + -5x + 1 Reorder the terms: 7000 = 1 + -5x + x2 Solving 7000 = 1 + -5x + x2 Solving for variable 'x'. Combine like terms: 7000 + -1 = 6999 6999 + 5x + -1x2 = 1 + -5x + x2 + -1 + 5x + -1x2 Reorder the terms: 6999 + 5x + -1x2 = 1 + -1 + -5x + 5x + x2 + -1x2 Combine like terms: 1 + -1 = 0 6999 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2 6999 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 6999 + 5x + -1x2 = 0 + x2 + -1x2 6999 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6999 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6999 + -5x + x2 = 0 Move the constant term to the right: Add '6999' to each side of the equation. -6999 + -5x + 6999 + x2 = 0 + 6999 Reorder the terms: -6999 + 6999 + -5x + x2 = 0 + 6999 Combine like terms: -6999 + 6999 = 0 0 + -5x + x2 = 0 + 6999 -5x + x2 = 0 + 6999 Combine like terms: 0 + 6999 = 6999 -5x + x2 = 6999 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 6999 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 6999 + 6.25 Combine like terms: 6999 + 6.25 = 7005.25 6.25 + -5x + x2 = 7005.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7005.25 Calculate the square root of the right side: 83.697371524 Break this problem into two subproblems by setting (x + -2.5) equal to 83.697371524 and -83.697371524.Subproblem 1
x + -2.5 = 83.697371524 Simplifying x + -2.5 = 83.697371524 Reorder the terms: -2.5 + x = 83.697371524 Solving -2.5 + x = 83.697371524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 83.697371524 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 83.697371524 + 2.5 x = 83.697371524 + 2.5 Combine like terms: 83.697371524 + 2.5 = 86.197371524 x = 86.197371524 Simplifying x = 86.197371524Subproblem 2
x + -2.5 = -83.697371524 Simplifying x + -2.5 = -83.697371524 Reorder the terms: -2.5 + x = -83.697371524 Solving -2.5 + x = -83.697371524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -83.697371524 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -83.697371524 + 2.5 x = -83.697371524 + 2.5 Combine like terms: -83.697371524 + 2.5 = -81.197371524 x = -81.197371524 Simplifying x = -81.197371524Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.197371524, -81.197371524}
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