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Simplifying x2 + -400x + 1 = 0 Reorder the terms: 1 + -400x + x2 = 0 Solving 1 + -400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -400x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -400x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -400x + x2 = 0 + -1 -400x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -400x + x2 = -1 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 = -1 + 40000 Reorder the terms: 40000 + -400x + x2 = -1 + 40000 Combine like terms: -1 + 40000 = 39999 40000 + -400x + x2 = 39999 Factor a perfect square on the left side: (x + -200)(x + -200) = 39999 Calculate the square root of the right side: 199.997499984 Break this problem into two subproblems by setting (x + -200) equal to 199.997499984 and -199.997499984.Subproblem 1
x + -200 = 199.997499984 Simplifying x + -200 = 199.997499984 Reorder the terms: -200 + x = 199.997499984 Solving -200 + x = 199.997499984 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 = 199.997499984 + 200 Combine like terms: -200 + 200 = 0 0 + x = 199.997499984 + 200 x = 199.997499984 + 200 Combine like terms: 199.997499984 + 200 = 399.997499984 x = 399.997499984 Simplifying x = 399.997499984Subproblem 2
x + -200 = -199.997499984 Simplifying x + -200 = -199.997499984 Reorder the terms: -200 + x = -199.997499984 Solving -200 + x = -199.997499984 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 = -199.997499984 + 200 Combine like terms: -200 + 200 = 0 0 + x = -199.997499984 + 200 x = -199.997499984 + 200 Combine like terms: -199.997499984 + 200 = 0.002500016 x = 0.002500016 Simplifying x = 0.002500016Solution
The solution to the problem is based on the solutions from the subproblems. x = {399.997499984, 0.002500016}
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