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Simplifying x2 + 500x + 100 = 0 Reorder the terms: 100 + 500x + x2 = 0 Solving 100 + 500x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 500x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 500x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 500x + x2 = 0 + -100 500x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 500x + x2 = -100 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = -100 + 62500 Reorder the terms: 62500 + 500x + x2 = -100 + 62500 Combine like terms: -100 + 62500 = 62400 62500 + 500x + x2 = 62400 Factor a perfect square on the left side: (x + 250)(x + 250) = 62400 Calculate the square root of the right side: 249.799919936 Break this problem into two subproblems by setting (x + 250) equal to 249.799919936 and -249.799919936.Subproblem 1
x + 250 = 249.799919936 Simplifying x + 250 = 249.799919936 Reorder the terms: 250 + x = 249.799919936 Solving 250 + x = 249.799919936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 249.799919936 + -250 Combine like terms: 250 + -250 = 0 0 + x = 249.799919936 + -250 x = 249.799919936 + -250 Combine like terms: 249.799919936 + -250 = -0.200080064 x = -0.200080064 Simplifying x = -0.200080064Subproblem 2
x + 250 = -249.799919936 Simplifying x + 250 = -249.799919936 Reorder the terms: 250 + x = -249.799919936 Solving 250 + x = -249.799919936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -249.799919936 + -250 Combine like terms: 250 + -250 = 0 0 + x = -249.799919936 + -250 x = -249.799919936 + -250 Combine like terms: -249.799919936 + -250 = -499.799919936 x = -499.799919936 Simplifying x = -499.799919936Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.200080064, -499.799919936}
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