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Simplifying x2 + 191x + -2669.225 = 0 Reorder the terms: -2669.225 + 191x + x2 = 0 Solving -2669.225 + 191x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2669.225' to each side of the equation. -2669.225 + 191x + 2669.225 + x2 = 0 + 2669.225 Reorder the terms: -2669.225 + 2669.225 + 191x + x2 = 0 + 2669.225 Combine like terms: -2669.225 + 2669.225 = 0.000 0.000 + 191x + x2 = 0 + 2669.225 191x + x2 = 0 + 2669.225 Combine like terms: 0 + 2669.225 = 2669.225 191x + x2 = 2669.225 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 = 2669.225 + 9120.25 Reorder the terms: 9120.25 + 191x + x2 = 2669.225 + 9120.25 Combine like terms: 2669.225 + 9120.25 = 11789.475 9120.25 + 191x + x2 = 11789.475 Factor a perfect square on the left side: (x + 95.5)(x + 95.5) = 11789.475 Calculate the square root of the right side: 108.579348865 Break this problem into two subproblems by setting (x + 95.5) equal to 108.579348865 and -108.579348865.Subproblem 1
x + 95.5 = 108.579348865 Simplifying x + 95.5 = 108.579348865 Reorder the terms: 95.5 + x = 108.579348865 Solving 95.5 + x = 108.579348865 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 = 108.579348865 + -95.5 Combine like terms: 95.5 + -95.5 = 0.0 0.0 + x = 108.579348865 + -95.5 x = 108.579348865 + -95.5 Combine like terms: 108.579348865 + -95.5 = 13.079348865 x = 13.079348865 Simplifying x = 13.079348865Subproblem 2
x + 95.5 = -108.579348865 Simplifying x + 95.5 = -108.579348865 Reorder the terms: 95.5 + x = -108.579348865 Solving 95.5 + x = -108.579348865 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 = -108.579348865 + -95.5 Combine like terms: 95.5 + -95.5 = 0.0 0.0 + x = -108.579348865 + -95.5 x = -108.579348865 + -95.5 Combine like terms: -108.579348865 + -95.5 = -204.079348865 x = -204.079348865 Simplifying x = -204.079348865Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.079348865, -204.079348865}
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