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Simplifying 2X2 + 9X + -34 = 0 Reorder the terms: -34 + 9X + 2X2 = 0 Solving -34 + 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'. -17 + 4.5X + X2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 4.5X + 17 + X2 = 0 + 17 Reorder the terms: -17 + 17 + 4.5X + X2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 4.5X + X2 = 0 + 17 4.5X + X2 = 0 + 17 Combine like terms: 0 + 17 = 17 4.5X + X2 = 17 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 = 17 + 5.0625 Reorder the terms: 5.0625 + 4.5X + X2 = 17 + 5.0625 Combine like terms: 17 + 5.0625 = 22.0625 5.0625 + 4.5X + X2 = 22.0625 Factor a perfect square on the left side: (X + 2.25)(X + 2.25) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (X + 2.25) equal to 4.697073557 and -4.697073557.Subproblem 1
X + 2.25 = 4.697073557 Simplifying X + 2.25 = 4.697073557 Reorder the terms: 2.25 + X = 4.697073557 Solving 2.25 + X = 4.697073557 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 = 4.697073557 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = 4.697073557 + -2.25 X = 4.697073557 + -2.25 Combine like terms: 4.697073557 + -2.25 = 2.447073557 X = 2.447073557 Simplifying X = 2.447073557Subproblem 2
X + 2.25 = -4.697073557 Simplifying X + 2.25 = -4.697073557 Reorder the terms: 2.25 + X = -4.697073557 Solving 2.25 + X = -4.697073557 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 = -4.697073557 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = -4.697073557 + -2.25 X = -4.697073557 + -2.25 Combine like terms: -4.697073557 + -2.25 = -6.947073557 X = -6.947073557 Simplifying X = -6.947073557Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.447073557, -6.947073557}
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