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Simplifying X2 + 9X + -82 = 0 Reorder the terms: -82 + 9X + X2 = 0 Solving -82 + 9X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + 9X + 82 + X2 = 0 + 82 Reorder the terms: -82 + 82 + 9X + X2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 9X + X2 = 0 + 82 9X + X2 = 0 + 82 Combine like terms: 0 + 82 = 82 9X + X2 = 82 The X term is 9X. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9X + 20.25 + X2 = 82 + 20.25 Reorder the terms: 20.25 + 9X + X2 = 82 + 20.25 Combine like terms: 82 + 20.25 = 102.25 20.25 + 9X + X2 = 102.25 Factor a perfect square on the left side: (X + 4.5)(X + 4.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (X + 4.5) equal to 10.111874208 and -10.111874208.Subproblem 1
X + 4.5 = 10.111874208 Simplifying X + 4.5 = 10.111874208 Reorder the terms: 4.5 + X = 10.111874208 Solving 4.5 + X = 10.111874208 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + X = 10.111874208 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = 10.111874208 + -4.5 X = 10.111874208 + -4.5 Combine like terms: 10.111874208 + -4.5 = 5.611874208 X = 5.611874208 Simplifying X = 5.611874208Subproblem 2
X + 4.5 = -10.111874208 Simplifying X + 4.5 = -10.111874208 Reorder the terms: 4.5 + X = -10.111874208 Solving 4.5 + X = -10.111874208 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + X = -10.111874208 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = -10.111874208 + -4.5 X = -10.111874208 + -4.5 Combine like terms: -10.111874208 + -4.5 = -14.611874208 X = -14.611874208 Simplifying X = -14.611874208Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.611874208, -14.611874208}
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