x^2+22x=9

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Solution for x^2+22x=9 equation:


Simplifying
x2 + 22x = 9

Reorder the terms:
22x + x2 = 9

Solving
22x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 22x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 22x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 22x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 22x + x2 = 0 + 9
22x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
22x + x2 = 9

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 = 9 + 121

Reorder the terms:
121 + 22x + x2 = 9 + 121

Combine like terms: 9 + 121 = 130
121 + 22x + x2 = 130

Factor a perfect square on the left side:
(x + 11)(x + 11) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(x + 11) equal to 11.401754251 and -11.401754251.

Subproblem 1

x + 11 = 11.401754251 Simplifying x + 11 = 11.401754251 Reorder the terms: 11 + x = 11.401754251 Solving 11 + x = 11.401754251 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 = 11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.401754251 + -11 x = 11.401754251 + -11 Combine like terms: 11.401754251 + -11 = 0.401754251 x = 0.401754251 Simplifying x = 0.401754251

Subproblem 2

x + 11 = -11.401754251 Simplifying x + 11 = -11.401754251 Reorder the terms: 11 + x = -11.401754251 Solving 11 + x = -11.401754251 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 = -11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.401754251 + -11 x = -11.401754251 + -11 Combine like terms: -11.401754251 + -11 = -22.401754251 x = -22.401754251 Simplifying x = -22.401754251

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.401754251, -22.401754251}

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