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Simplifying x2 + 191x + -3845.75 = 0 Reorder the terms: -3845.75 + 191x + x2 = 0 Solving -3845.75 + 191x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3845.75' to each side of the equation. -3845.75 + 191x + 3845.75 + x2 = 0 + 3845.75 Reorder the terms: -3845.75 + 3845.75 + 191x + x2 = 0 + 3845.75 Combine like terms: -3845.75 + 3845.75 = 0.00 0.00 + 191x + x2 = 0 + 3845.75 191x + x2 = 0 + 3845.75 Combine like terms: 0 + 3845.75 = 3845.75 191x + x2 = 3845.75 The x term is 191x. Take half its coefficient (95.5). Square it (9120.25) and add it to both sides. Add '9120.25' to each side of the equation. 191x + 9120.25 + x2 = 3845.75 + 9120.25 Reorder the terms: 9120.25 + 191x + x2 = 3845.75 + 9120.25 Combine like terms: 3845.75 + 9120.25 = 12966 9120.25 + 191x + x2 = 12966 Factor a perfect square on the left side: (x + 95.5)(x + 95.5) = 12966 Calculate the square root of the right side: 113.868345031 Break this problem into two subproblems by setting (x + 95.5) equal to 113.868345031 and -113.868345031.Subproblem 1
x + 95.5 = 113.868345031 Simplifying x + 95.5 = 113.868345031 Reorder the terms: 95.5 + x = 113.868345031 Solving 95.5 + x = 113.868345031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95.5' to each side of the equation. 95.5 + -95.5 + x = 113.868345031 + -95.5 Combine like terms: 95.5 + -95.5 = 0.0 0.0 + x = 113.868345031 + -95.5 x = 113.868345031 + -95.5 Combine like terms: 113.868345031 + -95.5 = 18.368345031 x = 18.368345031 Simplifying x = 18.368345031Subproblem 2
x + 95.5 = -113.868345031 Simplifying x + 95.5 = -113.868345031 Reorder the terms: 95.5 + x = -113.868345031 Solving 95.5 + x = -113.868345031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95.5' to each side of the equation. 95.5 + -95.5 + x = -113.868345031 + -95.5 Combine like terms: 95.5 + -95.5 = 0.0 0.0 + x = -113.868345031 + -95.5 x = -113.868345031 + -95.5 Combine like terms: -113.868345031 + -95.5 = -209.368345031 x = -209.368345031 Simplifying x = -209.368345031Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.368345031, -209.368345031}
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