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Simplifying x2 + 600x + 64375 = 0 Reorder the terms: 64375 + 600x + x2 = 0 Solving 64375 + 600x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64375' to each side of the equation. 64375 + 600x + -64375 + x2 = 0 + -64375 Reorder the terms: 64375 + -64375 + 600x + x2 = 0 + -64375 Combine like terms: 64375 + -64375 = 0 0 + 600x + x2 = 0 + -64375 600x + x2 = 0 + -64375 Combine like terms: 0 + -64375 = -64375 600x + x2 = -64375 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = -64375 + 90000 Reorder the terms: 90000 + 600x + x2 = -64375 + 90000 Combine like terms: -64375 + 90000 = 25625 90000 + 600x + x2 = 25625 Factor a perfect square on the left side: (x + 300)(x + 300) = 25625 Calculate the square root of the right side: 160.078105936 Break this problem into two subproblems by setting (x + 300) equal to 160.078105936 and -160.078105936.Subproblem 1
x + 300 = 160.078105936 Simplifying x + 300 = 160.078105936 Reorder the terms: 300 + x = 160.078105936 Solving 300 + x = 160.078105936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 160.078105936 + -300 Combine like terms: 300 + -300 = 0 0 + x = 160.078105936 + -300 x = 160.078105936 + -300 Combine like terms: 160.078105936 + -300 = -139.921894064 x = -139.921894064 Simplifying x = -139.921894064Subproblem 2
x + 300 = -160.078105936 Simplifying x + 300 = -160.078105936 Reorder the terms: 300 + x = -160.078105936 Solving 300 + x = -160.078105936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -160.078105936 + -300 Combine like terms: 300 + -300 = 0 0 + x = -160.078105936 + -300 x = -160.078105936 + -300 Combine like terms: -160.078105936 + -300 = -460.078105936 x = -460.078105936 Simplifying x = -460.078105936Solution
The solution to the problem is based on the solutions from the subproblems. x = {-139.921894064, -460.078105936}
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