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Simplifying x2 + 22x + 44 = 0 Reorder the terms: 44 + 22x + x2 = 0 Solving 44 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + 22x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + 22x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 22x + x2 = 0 + -44 22x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 22x + x2 = -44 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 = -44 + 121 Reorder the terms: 121 + 22x + x2 = -44 + 121 Combine like terms: -44 + 121 = 77 121 + 22x + x2 = 77 Factor a perfect square on the left side: (x + 11)(x + 11) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + 11) equal to 8.774964387 and -8.774964387.Subproblem 1
x + 11 = 8.774964387 Simplifying x + 11 = 8.774964387 Reorder the terms: 11 + x = 8.774964387 Solving 11 + x = 8.774964387 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 = 8.774964387 + -11 Combine like terms: 11 + -11 = 0 0 + x = 8.774964387 + -11 x = 8.774964387 + -11 Combine like terms: 8.774964387 + -11 = -2.225035613 x = -2.225035613 Simplifying x = -2.225035613Subproblem 2
x + 11 = -8.774964387 Simplifying x + 11 = -8.774964387 Reorder the terms: 11 + x = -8.774964387 Solving 11 + x = -8.774964387 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 = -8.774964387 + -11 Combine like terms: 11 + -11 = 0 0 + x = -8.774964387 + -11 x = -8.774964387 + -11 Combine like terms: -8.774964387 + -11 = -19.774964387 x = -19.774964387 Simplifying x = -19.774964387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.225035613, -19.774964387}
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