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Simplifying x2 + 8x + -10000 = 0 Reorder the terms: -10000 + 8x + x2 = 0 Solving -10000 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 8x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 8x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 8x + x2 = 0 + 10000 8x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 8x + x2 = 10000 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 = 10000 + 16 Reorder the terms: 16 + 8x + x2 = 10000 + 16 Combine like terms: 10000 + 16 = 10016 16 + 8x + x2 = 10016 Factor a perfect square on the left side: (x + 4)(x + 4) = 10016 Calculate the square root of the right side: 100.079968026 Break this problem into two subproblems by setting (x + 4) equal to 100.079968026 and -100.079968026.Subproblem 1
x + 4 = 100.079968026 Simplifying x + 4 = 100.079968026 Reorder the terms: 4 + x = 100.079968026 Solving 4 + x = 100.079968026 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 = 100.079968026 + -4 Combine like terms: 4 + -4 = 0 0 + x = 100.079968026 + -4 x = 100.079968026 + -4 Combine like terms: 100.079968026 + -4 = 96.079968026 x = 96.079968026 Simplifying x = 96.079968026Subproblem 2
x + 4 = -100.079968026 Simplifying x + 4 = -100.079968026 Reorder the terms: 4 + x = -100.079968026 Solving 4 + x = -100.079968026 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 = -100.079968026 + -4 Combine like terms: 4 + -4 = 0 0 + x = -100.079968026 + -4 x = -100.079968026 + -4 Combine like terms: -100.079968026 + -4 = -104.079968026 x = -104.079968026 Simplifying x = -104.079968026Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.079968026, -104.079968026}
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