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Simplifying x2 + -202x + 200 = 0 Reorder the terms: 200 + -202x + x2 = 0 Solving 200 + -202x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -202x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -202x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -202x + x2 = 0 + -200 -202x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -202x + x2 = -200 The x term is -202x. Take half its coefficient (-101). Square it (10201) and add it to both sides. Add '10201' to each side of the equation. -202x + 10201 + x2 = -200 + 10201 Reorder the terms: 10201 + -202x + x2 = -200 + 10201 Combine like terms: -200 + 10201 = 10001 10201 + -202x + x2 = 10001 Factor a perfect square on the left side: (x + -101)(x + -101) = 10001 Calculate the square root of the right side: 100.004999875 Break this problem into two subproblems by setting (x + -101) equal to 100.004999875 and -100.004999875.Subproblem 1
x + -101 = 100.004999875 Simplifying x + -101 = 100.004999875 Reorder the terms: -101 + x = 100.004999875 Solving -101 + x = 100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = 100.004999875 + 101 Combine like terms: -101 + 101 = 0 0 + x = 100.004999875 + 101 x = 100.004999875 + 101 Combine like terms: 100.004999875 + 101 = 201.004999875 x = 201.004999875 Simplifying x = 201.004999875Subproblem 2
x + -101 = -100.004999875 Simplifying x + -101 = -100.004999875 Reorder the terms: -101 + x = -100.004999875 Solving -101 + x = -100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = -100.004999875 + 101 Combine like terms: -101 + 101 = 0 0 + x = -100.004999875 + 101 x = -100.004999875 + 101 Combine like terms: -100.004999875 + 101 = 0.995000125 x = 0.995000125 Simplifying x = 0.995000125Solution
The solution to the problem is based on the solutions from the subproblems. x = {201.004999875, 0.995000125}
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