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Simplifying 11x2 + 22x + 4 = 0 Reorder the terms: 4 + 22x + 11x2 = 0 Solving 4 + 22x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.3636363636 + 2x + x2 = 0 Move the constant term to the right: Add '-0.3636363636' to each side of the equation. 0.3636363636 + 2x + -0.3636363636 + x2 = 0 + -0.3636363636 Reorder the terms: 0.3636363636 + -0.3636363636 + 2x + x2 = 0 + -0.3636363636 Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.3636363636 2x + x2 = 0 + -0.3636363636 Combine like terms: 0 + -0.3636363636 = -0.3636363636 2x + x2 = -0.3636363636 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.3636363636 + 1 Reorder the terms: 1 + 2x + x2 = -0.3636363636 + 1 Combine like terms: -0.3636363636 + 1 = 0.6363636364 1 + 2x + x2 = 0.6363636364 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.6363636364 Calculate the square root of the right side: 0.797724035 Break this problem into two subproblems by setting (x + 1) equal to 0.797724035 and -0.797724035.Subproblem 1
x + 1 = 0.797724035 Simplifying x + 1 = 0.797724035 Reorder the terms: 1 + x = 0.797724035 Solving 1 + x = 0.797724035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.797724035 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.797724035 + -1 x = 0.797724035 + -1 Combine like terms: 0.797724035 + -1 = -0.202275965 x = -0.202275965 Simplifying x = -0.202275965Subproblem 2
x + 1 = -0.797724035 Simplifying x + 1 = -0.797724035 Reorder the terms: 1 + x = -0.797724035 Solving 1 + x = -0.797724035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.797724035 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.797724035 + -1 x = -0.797724035 + -1 Combine like terms: -0.797724035 + -1 = -1.797724035 x = -1.797724035 Simplifying x = -1.797724035Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.202275965, -1.797724035}
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