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Simplifying 11x2 + 22x = 2 Reorder the terms: 22x + 11x2 = 2 Solving 22x + 11x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 22x + 11x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 22x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + 2x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 2x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 2x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.1818181818 2x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 2x + x2 = 0.1818181818 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 = 0.1818181818 + 1 Reorder the terms: 1 + 2x + x2 = 0.1818181818 + 1 Combine like terms: 0.1818181818 + 1 = 1.1818181818 1 + 2x + x2 = 1.1818181818 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.1818181818 Calculate the square root of the right side: 1.087114613 Break this problem into two subproblems by setting (x + 1) equal to 1.087114613 and -1.087114613.Subproblem 1
x + 1 = 1.087114613 Simplifying x + 1 = 1.087114613 Reorder the terms: 1 + x = 1.087114613 Solving 1 + x = 1.087114613 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 = 1.087114613 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.087114613 + -1 x = 1.087114613 + -1 Combine like terms: 1.087114613 + -1 = 0.087114613 x = 0.087114613 Simplifying x = 0.087114613Subproblem 2
x + 1 = -1.087114613 Simplifying x + 1 = -1.087114613 Reorder the terms: 1 + x = -1.087114613 Solving 1 + x = -1.087114613 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 = -1.087114613 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.087114613 + -1 x = -1.087114613 + -1 Combine like terms: -1.087114613 + -1 = -2.087114613 x = -2.087114613 Simplifying x = -2.087114613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.087114613, -2.087114613}
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