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Simplifying x2 + 400x + -45000 = 0 Reorder the terms: -45000 + 400x + x2 = 0 Solving -45000 + 400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45000' to each side of the equation. -45000 + 400x + 45000 + x2 = 0 + 45000 Reorder the terms: -45000 + 45000 + 400x + x2 = 0 + 45000 Combine like terms: -45000 + 45000 = 0 0 + 400x + x2 = 0 + 45000 400x + x2 = 0 + 45000 Combine like terms: 0 + 45000 = 45000 400x + x2 = 45000 The x term is 400x. Take half its coefficient (200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. 400x + 40000 + x2 = 45000 + 40000 Reorder the terms: 40000 + 400x + x2 = 45000 + 40000 Combine like terms: 45000 + 40000 = 85000 40000 + 400x + x2 = 85000 Factor a perfect square on the left side: (x + 200)(x + 200) = 85000 Calculate the square root of the right side: 291.547594742 Break this problem into two subproblems by setting (x + 200) equal to 291.547594742 and -291.547594742.Subproblem 1
x + 200 = 291.547594742 Simplifying x + 200 = 291.547594742 Reorder the terms: 200 + x = 291.547594742 Solving 200 + x = 291.547594742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = 291.547594742 + -200 Combine like terms: 200 + -200 = 0 0 + x = 291.547594742 + -200 x = 291.547594742 + -200 Combine like terms: 291.547594742 + -200 = 91.547594742 x = 91.547594742 Simplifying x = 91.547594742Subproblem 2
x + 200 = -291.547594742 Simplifying x + 200 = -291.547594742 Reorder the terms: 200 + x = -291.547594742 Solving 200 + x = -291.547594742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = -291.547594742 + -200 Combine like terms: 200 + -200 = 0 0 + x = -291.547594742 + -200 x = -291.547594742 + -200 Combine like terms: -291.547594742 + -200 = -491.547594742 x = -491.547594742 Simplifying x = -491.547594742Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.547594742, -491.547594742}
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