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Simplifying x2 + 10x + -8000 = 0 Reorder the terms: -8000 + 10x + x2 = 0 Solving -8000 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8000' to each side of the equation. -8000 + 10x + 8000 + x2 = 0 + 8000 Reorder the terms: -8000 + 8000 + 10x + x2 = 0 + 8000 Combine like terms: -8000 + 8000 = 0 0 + 10x + x2 = 0 + 8000 10x + x2 = 0 + 8000 Combine like terms: 0 + 8000 = 8000 10x + x2 = 8000 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 8000 + 25 Reorder the terms: 25 + 10x + x2 = 8000 + 25 Combine like terms: 8000 + 25 = 8025 25 + 10x + x2 = 8025 Factor a perfect square on the left side: (x + 5)(x + 5) = 8025 Calculate the square root of the right side: 89.582364336 Break this problem into two subproblems by setting (x + 5) equal to 89.582364336 and -89.582364336.Subproblem 1
x + 5 = 89.582364336 Simplifying x + 5 = 89.582364336 Reorder the terms: 5 + x = 89.582364336 Solving 5 + x = 89.582364336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 89.582364336 + -5 Combine like terms: 5 + -5 = 0 0 + x = 89.582364336 + -5 x = 89.582364336 + -5 Combine like terms: 89.582364336 + -5 = 84.582364336 x = 84.582364336 Simplifying x = 84.582364336Subproblem 2
x + 5 = -89.582364336 Simplifying x + 5 = -89.582364336 Reorder the terms: 5 + x = -89.582364336 Solving 5 + x = -89.582364336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -89.582364336 + -5 Combine like terms: 5 + -5 = 0 0 + x = -89.582364336 + -5 x = -89.582364336 + -5 Combine like terms: -89.582364336 + -5 = -94.582364336 x = -94.582364336 Simplifying x = -94.582364336Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.582364336, -94.582364336}
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