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Simplifying 2X2 + -9X + 3 = 0 Reorder the terms: 3 + -9X + 2X2 = 0 Solving 3 + -9X + 2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -4.5X + X2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4.5X + -1.5 + X2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4.5X + X2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4.5X + X2 = 0 + -1.5 -4.5X + X2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4.5X + X2 = -1.5 The X term is -4.5X. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5X + 5.0625 + X2 = -1.5 + 5.0625 Reorder the terms: 5.0625 + -4.5X + X2 = -1.5 + 5.0625 Combine like terms: -1.5 + 5.0625 = 3.5625 5.0625 + -4.5X + X2 = 3.5625 Factor a perfect square on the left side: (X + -2.25)(X + -2.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (X + -2.25) equal to 1.887458609 and -1.887458609.Subproblem 1
X + -2.25 = 1.887458609 Simplifying X + -2.25 = 1.887458609 Reorder the terms: -2.25 + X = 1.887458609 Solving -2.25 + X = 1.887458609 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + X = 1.887458609 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = 1.887458609 + 2.25 X = 1.887458609 + 2.25 Combine like terms: 1.887458609 + 2.25 = 4.137458609 X = 4.137458609 Simplifying X = 4.137458609Subproblem 2
X + -2.25 = -1.887458609 Simplifying X + -2.25 = -1.887458609 Reorder the terms: -2.25 + X = -1.887458609 Solving -2.25 + X = -1.887458609 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + X = -1.887458609 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = -1.887458609 + 2.25 X = -1.887458609 + 2.25 Combine like terms: -1.887458609 + 2.25 = 0.362541391 X = 0.362541391 Simplifying X = 0.362541391Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.137458609, 0.362541391}
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