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Simplifying x2 + 400x + -40000 = 0 Reorder the terms: -40000 + 400x + x2 = 0 Solving -40000 + 400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40000' to each side of the equation. -40000 + 400x + 40000 + x2 = 0 + 40000 Reorder the terms: -40000 + 40000 + 400x + x2 = 0 + 40000 Combine like terms: -40000 + 40000 = 0 0 + 400x + x2 = 0 + 40000 400x + x2 = 0 + 40000 Combine like terms: 0 + 40000 = 40000 400x + x2 = 40000 The x term is 400x. Take half its coefficient (200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. 400x + 40000 + x2 = 40000 + 40000 Reorder the terms: 40000 + 400x + x2 = 40000 + 40000 Combine like terms: 40000 + 40000 = 80000 40000 + 400x + x2 = 80000 Factor a perfect square on the left side: (x + 200)(x + 200) = 80000 Calculate the square root of the right side: 282.842712475 Break this problem into two subproblems by setting (x + 200) equal to 282.842712475 and -282.842712475.Subproblem 1
x + 200 = 282.842712475 Simplifying x + 200 = 282.842712475 Reorder the terms: 200 + x = 282.842712475 Solving 200 + x = 282.842712475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = 282.842712475 + -200 Combine like terms: 200 + -200 = 0 0 + x = 282.842712475 + -200 x = 282.842712475 + -200 Combine like terms: 282.842712475 + -200 = 82.842712475 x = 82.842712475 Simplifying x = 82.842712475Subproblem 2
x + 200 = -282.842712475 Simplifying x + 200 = -282.842712475 Reorder the terms: 200 + x = -282.842712475 Solving 200 + x = -282.842712475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = -282.842712475 + -200 Combine like terms: 200 + -200 = 0 0 + x = -282.842712475 + -200 x = -282.842712475 + -200 Combine like terms: -282.842712475 + -200 = -482.842712475 x = -482.842712475 Simplifying x = -482.842712475Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.842712475, -482.842712475}
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