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Simplifying x2 + 200x + -25 = 0 Reorder the terms: -25 + 200x + x2 = 0 Solving -25 + 200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 200x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 200x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 200x + x2 = 0 + 25 200x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 200x + x2 = 25 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 = 25 + 10000 Reorder the terms: 10000 + 200x + x2 = 25 + 10000 Combine like terms: 25 + 10000 = 10025 10000 + 200x + x2 = 10025 Factor a perfect square on the left side: (x + 100)(x + 100) = 10025 Calculate the square root of the right side: 100.124921973 Break this problem into two subproblems by setting (x + 100) equal to 100.124921973 and -100.124921973.Subproblem 1
x + 100 = 100.124921973 Simplifying x + 100 = 100.124921973 Reorder the terms: 100 + x = 100.124921973 Solving 100 + x = 100.124921973 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 = 100.124921973 + -100 Combine like terms: 100 + -100 = 0 0 + x = 100.124921973 + -100 x = 100.124921973 + -100 Combine like terms: 100.124921973 + -100 = 0.124921973 x = 0.124921973 Simplifying x = 0.124921973Subproblem 2
x + 100 = -100.124921973 Simplifying x + 100 = -100.124921973 Reorder the terms: 100 + x = -100.124921973 Solving 100 + x = -100.124921973 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 = -100.124921973 + -100 Combine like terms: 100 + -100 = 0 0 + x = -100.124921973 + -100 x = -100.124921973 + -100 Combine like terms: -100.124921973 + -100 = -200.124921973 x = -200.124921973 Simplifying x = -200.124921973Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.124921973, -200.124921973}
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