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Simplifying x2 = 11x + 50 Reorder the terms: x2 = 50 + 11x Solving x2 = 50 + 11x Solving for variable 'x'. Reorder the terms: -50 + -11x + x2 = 50 + 11x + -50 + -11x Reorder the terms: -50 + -11x + x2 = 50 + -50 + 11x + -11x Combine like terms: 50 + -50 = 0 -50 + -11x + x2 = 0 + 11x + -11x -50 + -11x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -50 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -11x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -11x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -11x + x2 = 0 + 50 -11x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -11x + x2 = 50 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 50 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 50 + 30.25 Combine like terms: 50 + 30.25 = 80.25 30.25 + -11x + x2 = 80.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + -5.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + -5.5 = 8.958236434 Simplifying x + -5.5 = 8.958236434 Reorder the terms: -5.5 + x = 8.958236434 Solving -5.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 8.958236434 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.958236434 + 5.5 x = 8.958236434 + 5.5 Combine like terms: 8.958236434 + 5.5 = 14.458236434 x = 14.458236434 Simplifying x = 14.458236434Subproblem 2
x + -5.5 = -8.958236434 Simplifying x + -5.5 = -8.958236434 Reorder the terms: -5.5 + x = -8.958236434 Solving -5.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -8.958236434 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.958236434 + 5.5 x = -8.958236434 + 5.5 Combine like terms: -8.958236434 + 5.5 = -3.458236434 x = -3.458236434 Simplifying x = -3.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.458236434, -3.458236434}
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