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Simplifying 9X2 + 27X + 2 = 0 Reorder the terms: 2 + 27X + 9X2 = 0 Solving 2 + 27X + 9X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 3X + X2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 3X + -0.2222222222 + X2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 3X + X2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 3X + X2 = 0 + -0.2222222222 3X + X2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 3X + X2 = -0.2222222222 The X term is 3X. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3X + 2.25 + X2 = -0.2222222222 + 2.25 Reorder the terms: 2.25 + 3X + X2 = -0.2222222222 + 2.25 Combine like terms: -0.2222222222 + 2.25 = 2.0277777778 2.25 + 3X + X2 = 2.0277777778 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 2.0277777778 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (X + 1.5) equal to 1.424000624 and -1.424000624.Subproblem 1
X + 1.5 = 1.424000624 Simplifying X + 1.5 = 1.424000624 Reorder the terms: 1.5 + X = 1.424000624 Solving 1.5 + X = 1.424000624 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 1.424000624 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 1.424000624 + -1.5 X = 1.424000624 + -1.5 Combine like terms: 1.424000624 + -1.5 = -0.075999376 X = -0.075999376 Simplifying X = -0.075999376Subproblem 2
X + 1.5 = -1.424000624 Simplifying X + 1.5 = -1.424000624 Reorder the terms: 1.5 + X = -1.424000624 Solving 1.5 + X = -1.424000624 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -1.424000624 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -1.424000624 + -1.5 X = -1.424000624 + -1.5 Combine like terms: -1.424000624 + -1.5 = -2.924000624 X = -2.924000624 Simplifying X = -2.924000624Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.075999376, -2.924000624}
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