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Simplifying x2 + x + -30000 = 0 Reorder the terms: -30000 + x + x2 = 0 Solving -30000 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30000' to each side of the equation. -30000 + x + 30000 + x2 = 0 + 30000 Reorder the terms: -30000 + 30000 + x + x2 = 0 + 30000 Combine like terms: -30000 + 30000 = 0 0 + x + x2 = 0 + 30000 x + x2 = 0 + 30000 Combine like terms: 0 + 30000 = 30000 x + x2 = 30000 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 30000 + 0.25 Reorder the terms: 0.25 + x + x2 = 30000 + 0.25 Combine like terms: 30000 + 0.25 = 30000.25 0.25 + x + x2 = 30000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 30000.25 Calculate the square root of the right side: 173.205802443 Break this problem into two subproblems by setting (x + 0.5) equal to 173.205802443 and -173.205802443.Subproblem 1
x + 0.5 = 173.205802443 Simplifying x + 0.5 = 173.205802443 Reorder the terms: 0.5 + x = 173.205802443 Solving 0.5 + x = 173.205802443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 173.205802443 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 173.205802443 + -0.5 x = 173.205802443 + -0.5 Combine like terms: 173.205802443 + -0.5 = 172.705802443 x = 172.705802443 Simplifying x = 172.705802443Subproblem 2
x + 0.5 = -173.205802443 Simplifying x + 0.5 = -173.205802443 Reorder the terms: 0.5 + x = -173.205802443 Solving 0.5 + x = -173.205802443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -173.205802443 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -173.205802443 + -0.5 x = -173.205802443 + -0.5 Combine like terms: -173.205802443 + -0.5 = -173.705802443 x = -173.705802443 Simplifying x = -173.705802443Solution
The solution to the problem is based on the solutions from the subproblems. x = {172.705802443, -173.705802443}
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