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Simplifying x2 + -8x + -4000 = 0 Reorder the terms: -4000 + -8x + x2 = 0 Solving -4000 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -8x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + -8x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -8x + x2 = 0 + 4000 -8x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -8x + x2 = 4000 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 4000 + 16 Reorder the terms: 16 + -8x + x2 = 4000 + 16 Combine like terms: 4000 + 16 = 4016 16 + -8x + x2 = 4016 Factor a perfect square on the left side: (x + -4)(x + -4) = 4016 Calculate the square root of the right side: 63.371918071 Break this problem into two subproblems by setting (x + -4) equal to 63.371918071 and -63.371918071.Subproblem 1
x + -4 = 63.371918071 Simplifying x + -4 = 63.371918071 Reorder the terms: -4 + x = 63.371918071 Solving -4 + x = 63.371918071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 63.371918071 + 4 Combine like terms: -4 + 4 = 0 0 + x = 63.371918071 + 4 x = 63.371918071 + 4 Combine like terms: 63.371918071 + 4 = 67.371918071 x = 67.371918071 Simplifying x = 67.371918071Subproblem 2
x + -4 = -63.371918071 Simplifying x + -4 = -63.371918071 Reorder the terms: -4 + x = -63.371918071 Solving -4 + x = -63.371918071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -63.371918071 + 4 Combine like terms: -4 + 4 = 0 0 + x = -63.371918071 + 4 x = -63.371918071 + 4 Combine like terms: -63.371918071 + 4 = -59.371918071 x = -59.371918071 Simplifying x = -59.371918071Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.371918071, -59.371918071}
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