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Simplifying x2 + 999x + -32 = 0 Reorder the terms: -32 + 999x + x2 = 0 Solving -32 + 999x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 999x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 999x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 999x + x2 = 0 + 32 999x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 999x + x2 = 32 The x term is 999x. Take half its coefficient (499.5). Square it (249500.25) and add it to both sides. Add '249500.25' to each side of the equation. 999x + 249500.25 + x2 = 32 + 249500.25 Reorder the terms: 249500.25 + 999x + x2 = 32 + 249500.25 Combine like terms: 32 + 249500.25 = 249532.25 249500.25 + 999x + x2 = 249532.25 Factor a perfect square on the left side: (x + 499.5)(x + 499.5) = 249532.25 Calculate the square root of the right side: 499.532031005 Break this problem into two subproblems by setting (x + 499.5) equal to 499.532031005 and -499.532031005.Subproblem 1
x + 499.5 = 499.532031005 Simplifying x + 499.5 = 499.532031005 Reorder the terms: 499.5 + x = 499.532031005 Solving 499.5 + x = 499.532031005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-499.5' to each side of the equation. 499.5 + -499.5 + x = 499.532031005 + -499.5 Combine like terms: 499.5 + -499.5 = 0.0 0.0 + x = 499.532031005 + -499.5 x = 499.532031005 + -499.5 Combine like terms: 499.532031005 + -499.5 = 0.032031005 x = 0.032031005 Simplifying x = 0.032031005Subproblem 2
x + 499.5 = -499.532031005 Simplifying x + 499.5 = -499.532031005 Reorder the terms: 499.5 + x = -499.532031005 Solving 499.5 + x = -499.532031005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-499.5' to each side of the equation. 499.5 + -499.5 + x = -499.532031005 + -499.5 Combine like terms: 499.5 + -499.5 = 0.0 0.0 + x = -499.532031005 + -499.5 x = -499.532031005 + -499.5 Combine like terms: -499.532031005 + -499.5 = -999.032031005 x = -999.032031005 Simplifying x = -999.032031005Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.032031005, -999.032031005}
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