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Simplifying x2 + 10x + -4000 = 0 Reorder the terms: -4000 + 10x + x2 = 0 Solving -4000 + 10x + 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 + 10x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + 10x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + 10x + x2 = 0 + 4000 10x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 10x + x2 = 4000 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 = 4000 + 25 Reorder the terms: 25 + 10x + x2 = 4000 + 25 Combine like terms: 4000 + 25 = 4025 25 + 10x + x2 = 4025 Factor a perfect square on the left side: (x + 5)(x + 5) = 4025 Calculate the square root of the right side: 63.442887702 Break this problem into two subproblems by setting (x + 5) equal to 63.442887702 and -63.442887702.Subproblem 1
x + 5 = 63.442887702 Simplifying x + 5 = 63.442887702 Reorder the terms: 5 + x = 63.442887702 Solving 5 + x = 63.442887702 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 = 63.442887702 + -5 Combine like terms: 5 + -5 = 0 0 + x = 63.442887702 + -5 x = 63.442887702 + -5 Combine like terms: 63.442887702 + -5 = 58.442887702 x = 58.442887702 Simplifying x = 58.442887702Subproblem 2
x + 5 = -63.442887702 Simplifying x + 5 = -63.442887702 Reorder the terms: 5 + x = -63.442887702 Solving 5 + x = -63.442887702 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 = -63.442887702 + -5 Combine like terms: 5 + -5 = 0 0 + x = -63.442887702 + -5 x = -63.442887702 + -5 Combine like terms: -63.442887702 + -5 = -68.442887702 x = -68.442887702 Simplifying x = -68.442887702Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.442887702, -68.442887702}
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