x(2x+10)=22

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Solution for x(2x+10)=22 equation: 


Simplifying
x(2x + 10) = 22

Reorder the terms:
x(10 + 2x) = 22
(10 * x + 2x * x) = 22
(10x + 2x2) = 22

Solving
10x + 2x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 10x + 2x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-11 + 5x + x2 = 0

Solving
-11 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 5x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 5x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 5x + x2 = 0 + 11
5x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
5x + x2 = 11

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 11 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 11 + 6.25

Combine like terms: 11 + 6.25 = 17.25
6.25 + 5x + x2 = 17.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + 2.5 = 4.153311931

Simplifying
x + 2.5 = 4.153311931

Reorder the terms:
2.5 + x = 4.153311931

Solving
2.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.153311931 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.153311931 + -2.5
x = 4.153311931 + -2.5

Combine like terms: 4.153311931 + -2.5 = 1.653311931
x = 1.653311931

Simplifying
x = 1.653311931


Subproblem 2
x + 2.5 = -4.153311931

Simplifying
x + 2.5 = -4.153311931

Reorder the terms:
2.5 + x = -4.153311931

Solving
2.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.153311931 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.153311931 + -2.5
x = -4.153311931 + -2.5

Combine like terms: -4.153311931 + -2.5 = -6.653311931
x = -6.653311931

Simplifying
x = -6.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.653311931, -6.653311931}
Solution
x = {1.653311931, -6.653311931}

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