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Simplifying x2 + 22x + 20 = 0 Reorder the terms: 20 + 22x + x2 = 0 Solving 20 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 22x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 22x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 22x + x2 = 0 + -20 22x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 22x + x2 = -20 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 = -20 + 121 Reorder the terms: 121 + 22x + x2 = -20 + 121 Combine like terms: -20 + 121 = 101 121 + 22x + x2 = 101 Factor a perfect square on the left side: (x + 11)(x + 11) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 11) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 11 = 10.049875621 Simplifying x + 11 = 10.049875621 Reorder the terms: 11 + x = 10.049875621 Solving 11 + x = 10.049875621 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 = 10.049875621 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.049875621 + -11 x = 10.049875621 + -11 Combine like terms: 10.049875621 + -11 = -0.950124379 x = -0.950124379 Simplifying x = -0.950124379Subproblem 2
x + 11 = -10.049875621 Simplifying x + 11 = -10.049875621 Reorder the terms: 11 + x = -10.049875621 Solving 11 + x = -10.049875621 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 = -10.049875621 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.049875621 + -11 x = -10.049875621 + -11 Combine like terms: -10.049875621 + -11 = -21.049875621 x = -21.049875621 Simplifying x = -21.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.950124379, -21.049875621}
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