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Simplifying X2 + 9X + -98 = 129 Reorder the terms: -98 + 9X + X2 = 129 Solving -98 + 9X + X2 = 129 Solving for variable 'X'. Reorder the terms: -98 + -129 + 9X + X2 = 129 + -129 Combine like terms: -98 + -129 = -227 -227 + 9X + X2 = 129 + -129 Combine like terms: 129 + -129 = 0 -227 + 9X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '227' to each side of the equation. -227 + 9X + 227 + X2 = 0 + 227 Reorder the terms: -227 + 227 + 9X + X2 = 0 + 227 Combine like terms: -227 + 227 = 0 0 + 9X + X2 = 0 + 227 9X + X2 = 0 + 227 Combine like terms: 0 + 227 = 227 9X + X2 = 227 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 = 227 + 20.25 Reorder the terms: 20.25 + 9X + X2 = 227 + 20.25 Combine like terms: 227 + 20.25 = 247.25 20.25 + 9X + X2 = 247.25 Factor a perfect square on the left side: (X + 4.5)(X + 4.5) = 247.25 Calculate the square root of the right side: 15.724185194 Break this problem into two subproblems by setting (X + 4.5) equal to 15.724185194 and -15.724185194.Subproblem 1
X + 4.5 = 15.724185194 Simplifying X + 4.5 = 15.724185194 Reorder the terms: 4.5 + X = 15.724185194 Solving 4.5 + X = 15.724185194 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 = 15.724185194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = 15.724185194 + -4.5 X = 15.724185194 + -4.5 Combine like terms: 15.724185194 + -4.5 = 11.224185194 X = 11.224185194 Simplifying X = 11.224185194Subproblem 2
X + 4.5 = -15.724185194 Simplifying X + 4.5 = -15.724185194 Reorder the terms: 4.5 + X = -15.724185194 Solving 4.5 + X = -15.724185194 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 = -15.724185194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = -15.724185194 + -4.5 X = -15.724185194 + -4.5 Combine like terms: -15.724185194 + -4.5 = -20.224185194 X = -20.224185194 Simplifying X = -20.224185194Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.224185194, -20.224185194}
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