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Simplifying 9x2 + 49x = 22 + -5x Reorder the terms: 49x + 9x2 = 22 + -5x Solving 49x + 9x2 = 22 + -5x Solving for variable 'x'. Reorder the terms: -22 + 49x + 5x + 9x2 = 22 + -5x + -22 + 5x Combine like terms: 49x + 5x = 54x -22 + 54x + 9x2 = 22 + -5x + -22 + 5x Reorder the terms: -22 + 54x + 9x2 = 22 + -22 + -5x + 5x Combine like terms: 22 + -22 = 0 -22 + 54x + 9x2 = 0 + -5x + 5x -22 + 54x + 9x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -22 + 54x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.444444444 + 6x + x2 = 0 Move the constant term to the right: Add '2.444444444' to each side of the equation. -2.444444444 + 6x + 2.444444444 + x2 = 0 + 2.444444444 Reorder the terms: -2.444444444 + 2.444444444 + 6x + x2 = 0 + 2.444444444 Combine like terms: -2.444444444 + 2.444444444 = 0.000000000 0.000000000 + 6x + x2 = 0 + 2.444444444 6x + x2 = 0 + 2.444444444 Combine like terms: 0 + 2.444444444 = 2.444444444 6x + x2 = 2.444444444 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2.444444444 + 9 Reorder the terms: 9 + 6x + x2 = 2.444444444 + 9 Combine like terms: 2.444444444 + 9 = 11.444444444 9 + 6x + x2 = 11.444444444 Factor a perfect square on the left side: (x + 3)(x + 3) = 11.444444444 Calculate the square root of the right side: 3.382963855 Break this problem into two subproblems by setting (x + 3) equal to 3.382963855 and -3.382963855.Subproblem 1
x + 3 = 3.382963855 Simplifying x + 3 = 3.382963855 Reorder the terms: 3 + x = 3.382963855 Solving 3 + x = 3.382963855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.382963855 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.382963855 + -3 x = 3.382963855 + -3 Combine like terms: 3.382963855 + -3 = 0.382963855 x = 0.382963855 Simplifying x = 0.382963855Subproblem 2
x + 3 = -3.382963855 Simplifying x + 3 = -3.382963855 Reorder the terms: 3 + x = -3.382963855 Solving 3 + x = -3.382963855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.382963855 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.382963855 + -3 x = -3.382963855 + -3 Combine like terms: -3.382963855 + -3 = -6.382963855 x = -6.382963855 Simplifying x = -6.382963855Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.382963855, -6.382963855}
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