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Simplifying x2 + -400x + 500 = 0 Reorder the terms: 500 + -400x + x2 = 0 Solving 500 + -400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -400x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -400x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -400x + x2 = 0 + -500 -400x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -400x + x2 = -500 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 = -500 + 40000 Reorder the terms: 40000 + -400x + x2 = -500 + 40000 Combine like terms: -500 + 40000 = 39500 40000 + -400x + x2 = 39500 Factor a perfect square on the left side: (x + -200)(x + -200) = 39500 Calculate the square root of the right side: 198.746069144 Break this problem into two subproblems by setting (x + -200) equal to 198.746069144 and -198.746069144.Subproblem 1
x + -200 = 198.746069144 Simplifying x + -200 = 198.746069144 Reorder the terms: -200 + x = 198.746069144 Solving -200 + x = 198.746069144 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 = 198.746069144 + 200 Combine like terms: -200 + 200 = 0 0 + x = 198.746069144 + 200 x = 198.746069144 + 200 Combine like terms: 198.746069144 + 200 = 398.746069144 x = 398.746069144 Simplifying x = 398.746069144Subproblem 2
x + -200 = -198.746069144 Simplifying x + -200 = -198.746069144 Reorder the terms: -200 + x = -198.746069144 Solving -200 + x = -198.746069144 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 = -198.746069144 + 200 Combine like terms: -200 + 200 = 0 0 + x = -198.746069144 + 200 x = -198.746069144 + 200 Combine like terms: -198.746069144 + 200 = 1.253930856 x = 1.253930856 Simplifying x = 1.253930856Solution
The solution to the problem is based on the solutions from the subproblems. x = {398.746069144, 1.253930856}
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