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Simplifying X2 + 11X + -50 = 0 Reorder the terms: -50 + 11X + X2 = 0 Solving -50 + 11X + X2 = 0 Solving for variable 'X'. 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 = 3.458236434 X = 3.458236434 Simplifying X = 3.458236434Subproblem 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 = -14.458236434 X = -14.458236434 Simplifying X = -14.458236434Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.458236434, -14.458236434}
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