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Simplifying 3(X2 + 3X + 4) = 44 Reorder the terms: 3(4 + 3X + X2) = 44 (4 * 3 + 3X * 3 + X2 * 3) = 44 (12 + 9X + 3X2) = 44 Solving 12 + 9X + 3X2 = 44 Solving for variable 'X'. Reorder the terms: 12 + -44 + 9X + 3X2 = 44 + -44 Combine like terms: 12 + -44 = -32 -32 + 9X + 3X2 = 44 + -44 Combine like terms: 44 + -44 = 0 -32 + 9X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + 3X + X2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 3X + 10.66666667 + X2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 3X + X2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 3X + X2 = 0 + 10.66666667 3X + X2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 3X + X2 = 10.66666667 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 = 10.66666667 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 10.66666667 + 2.25 Combine like terms: 10.66666667 + 2.25 = 12.91666667 2.25 + 3X + X2 = 12.91666667 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 12.91666667 Calculate the square root of the right side: 3.593976443 Break this problem into two subproblems by setting (X + 1.5) equal to 3.593976443 and -3.593976443.Subproblem 1
X + 1.5 = 3.593976443 Simplifying X + 1.5 = 3.593976443 Reorder the terms: 1.5 + X = 3.593976443 Solving 1.5 + X = 3.593976443 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 = 3.593976443 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 3.593976443 + -1.5 X = 3.593976443 + -1.5 Combine like terms: 3.593976443 + -1.5 = 2.093976443 X = 2.093976443 Simplifying X = 2.093976443Subproblem 2
X + 1.5 = -3.593976443 Simplifying X + 1.5 = -3.593976443 Reorder the terms: 1.5 + X = -3.593976443 Solving 1.5 + X = -3.593976443 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 = -3.593976443 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -3.593976443 + -1.5 X = -3.593976443 + -1.5 Combine like terms: -3.593976443 + -1.5 = -5.093976443 X = -5.093976443 Simplifying X = -5.093976443Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.093976443, -5.093976443}
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