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Simplifying x2 + 22x + 3 = 0 Reorder the terms: 3 + 22x + x2 = 0 Solving 3 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 22x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 22x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 22x + x2 = 0 + -3 22x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 22x + x2 = -3 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -3 + 121 Reorder the terms: 121 + 22x + x2 = -3 + 121 Combine like terms: -3 + 121 = 118 121 + 22x + x2 = 118 Factor a perfect square on the left side: (x + 11)(x + 11) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (x + 11) equal to 10.862780491 and -10.862780491.Subproblem 1
x + 11 = 10.862780491 Simplifying x + 11 = 10.862780491 Reorder the terms: 11 + x = 10.862780491 Solving 11 + x = 10.862780491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 10.862780491 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.862780491 + -11 x = 10.862780491 + -11 Combine like terms: 10.862780491 + -11 = -0.137219509 x = -0.137219509 Simplifying x = -0.137219509Subproblem 2
x + 11 = -10.862780491 Simplifying x + 11 = -10.862780491 Reorder the terms: 11 + x = -10.862780491 Solving 11 + x = -10.862780491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -10.862780491 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.862780491 + -11 x = -10.862780491 + -11 Combine like terms: -10.862780491 + -11 = -21.862780491 x = -21.862780491 Simplifying x = -21.862780491Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.137219509, -21.862780491}
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