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Simplifying x2 + -200x + -50 = 0 Reorder the terms: -50 + -200x + x2 = 0 Solving -50 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -200x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -200x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -200x + x2 = 0 + 50 -200x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -200x + x2 = 50 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = 50 + 10000 Reorder the terms: 10000 + -200x + x2 = 50 + 10000 Combine like terms: 50 + 10000 = 10050 10000 + -200x + x2 = 10050 Factor a perfect square on the left side: (x + -100)(x + -100) = 10050 Calculate the square root of the right side: 100.249688279 Break this problem into two subproblems by setting (x + -100) equal to 100.249688279 and -100.249688279.Subproblem 1
x + -100 = 100.249688279 Simplifying x + -100 = 100.249688279 Reorder the terms: -100 + x = 100.249688279 Solving -100 + x = 100.249688279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 100.249688279 + 100 Combine like terms: -100 + 100 = 0 0 + x = 100.249688279 + 100 x = 100.249688279 + 100 Combine like terms: 100.249688279 + 100 = 200.249688279 x = 200.249688279 Simplifying x = 200.249688279Subproblem 2
x + -100 = -100.249688279 Simplifying x + -100 = -100.249688279 Reorder the terms: -100 + x = -100.249688279 Solving -100 + x = -100.249688279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -100.249688279 + 100 Combine like terms: -100 + 100 = 0 0 + x = -100.249688279 + 100 x = -100.249688279 + 100 Combine like terms: -100.249688279 + 100 = -0.249688279 x = -0.249688279 Simplifying x = -0.249688279Solution
The solution to the problem is based on the solutions from the subproblems. x = {200.249688279, -0.249688279}
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