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Simplifying (7X2 + -1X + -2) + -1(9X2 + -5X + 2) + (4X2 + 3X + -6) = 0 Reorder the terms: (-2 + -1X + 7X2) + -1(9X2 + -5X + 2) + (4X2 + 3X + -6) = 0 Remove parenthesis around (-2 + -1X + 7X2) -2 + -1X + 7X2 + -1(9X2 + -5X + 2) + (4X2 + 3X + -6) = 0 Reorder the terms: -2 + -1X + 7X2 + -1(2 + -5X + 9X2) + (4X2 + 3X + -6) = 0 -2 + -1X + 7X2 + (2 * -1 + -5X * -1 + 9X2 * -1) + (4X2 + 3X + -6) = 0 -2 + -1X + 7X2 + (-2 + 5X + -9X2) + (4X2 + 3X + -6) = 0 Reorder the terms: -2 + -1X + 7X2 + -2 + 5X + -9X2 + (-6 + 3X + 4X2) = 0 Remove parenthesis around (-6 + 3X + 4X2) -2 + -1X + 7X2 + -2 + 5X + -9X2 + -6 + 3X + 4X2 = 0 Reorder the terms: -2 + -2 + -6 + -1X + 5X + 3X + 7X2 + -9X2 + 4X2 = 0 Combine like terms: -2 + -2 = -4 -4 + -6 + -1X + 5X + 3X + 7X2 + -9X2 + 4X2 = 0 Combine like terms: -4 + -6 = -10 -10 + -1X + 5X + 3X + 7X2 + -9X2 + 4X2 = 0 Combine like terms: -1X + 5X = 4X -10 + 4X + 3X + 7X2 + -9X2 + 4X2 = 0 Combine like terms: 4X + 3X = 7X -10 + 7X + 7X2 + -9X2 + 4X2 = 0 Combine like terms: 7X2 + -9X2 = -2X2 -10 + 7X + -2X2 + 4X2 = 0 Combine like terms: -2X2 + 4X2 = 2X2 -10 + 7X + 2X2 = 0 Solving -10 + 7X + 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'. -5 + 3.5X + X2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.5X + 5 + X2 = 0 + 5 Reorder the terms: -5 + 5 + 3.5X + X2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.5X + X2 = 0 + 5 3.5X + X2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.5X + X2 = 5 The X term is 3.5X. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5X + 3.0625 + X2 = 5 + 3.0625 Reorder the terms: 3.0625 + 3.5X + X2 = 5 + 3.0625 Combine like terms: 5 + 3.0625 = 8.0625 3.0625 + 3.5X + X2 = 8.0625 Factor a perfect square on the left side: (X + 1.75)(X + 1.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (X + 1.75) equal to 2.839454173 and -2.839454173.Subproblem 1
X + 1.75 = 2.839454173 Simplifying X + 1.75 = 2.839454173 Reorder the terms: 1.75 + X = 2.839454173 Solving 1.75 + X = 2.839454173 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + X = 2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + X = 2.839454173 + -1.75 X = 2.839454173 + -1.75 Combine like terms: 2.839454173 + -1.75 = 1.089454173 X = 1.089454173 Simplifying X = 1.089454173Subproblem 2
X + 1.75 = -2.839454173 Simplifying X + 1.75 = -2.839454173 Reorder the terms: 1.75 + X = -2.839454173 Solving 1.75 + X = -2.839454173 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + X = -2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + X = -2.839454173 + -1.75 X = -2.839454173 + -1.75 Combine like terms: -2.839454173 + -1.75 = -4.589454173 X = -4.589454173 Simplifying X = -4.589454173Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.089454173, -4.589454173}
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