x(2x+2)=22

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Solution for x(2x+2)=22 equation: 


Simplifying
x(2x + 2) = 22

Reorder the terms:
x(2 + 2x) = 22
(2 * x + 2x * x) = 22
(2x + 2x2) = 22

Solving
2x + 2x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 2x + 2x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + x + x2)' equal to zero and attempt to solve:

Simplifying
-11 + x + x2 = 0

Solving
-11 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x + x2 = 0 + 11
x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
x + x2 = 11

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 11 + 0.25

Reorder the terms:
0.25 + x + x2 = 11 + 0.25

Combine like terms: 11 + 0.25 = 11.25
0.25 + x + x2 = 11.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 0.5 = 3.354101966

Simplifying
x + 0.5 = 3.354101966

Reorder the terms:
0.5 + x = 3.354101966

Solving
0.5 + x = 3.354101966

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.354101966 + -0.5
x = 3.354101966 + -0.5

Combine like terms: 3.354101966 + -0.5 = 2.854101966
x = 2.854101966

Simplifying
x = 2.854101966


Subproblem 2
x + 0.5 = -3.354101966

Simplifying
x + 0.5 = -3.354101966

Reorder the terms:
0.5 + x = -3.354101966

Solving
0.5 + x = -3.354101966

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.354101966 + -0.5
x = -3.354101966 + -0.5

Combine like terms: -3.354101966 + -0.5 = -3.854101966
x = -3.854101966

Simplifying
x = -3.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.854101966, -3.854101966}
Solution
x = {2.854101966, -3.854101966}

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