x*(2x+2)=34

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Solution for x*(2x+2)=34 equation: 


Simplifying
x(2x + 2) = 34

Reorder the terms:
x(2 + 2x) = 34
(2 * x + 2x * x) = 34
(2x + 2x2) = 34

Solving
2x + 2x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + 2x + 2x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + x + x2 = 0

Solving
-17 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + x + x2 = 0 + 17
x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
x + x2 = 17

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 = 17 + 0.25

Reorder the terms:
0.25 + x + x2 = 17 + 0.25

Combine like terms: 17 + 0.25 = 17.25
0.25 + x + x2 = 17.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + 0.5 = 4.153311931

Simplifying
x + 0.5 = 4.153311931

Reorder the terms:
0.5 + x = 4.153311931

Solving
0.5 + x = 4.153311931

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 = 4.153311931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.153311931 + -0.5
x = 4.153311931 + -0.5

Combine like terms: 4.153311931 + -0.5 = 3.653311931
x = 3.653311931

Simplifying
x = 3.653311931


Subproblem 2
x + 0.5 = -4.153311931

Simplifying
x + 0.5 = -4.153311931

Reorder the terms:
0.5 + x = -4.153311931

Solving
0.5 + x = -4.153311931

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 = -4.153311931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.153311931 + -0.5
x = -4.153311931 + -0.5

Combine like terms: -4.153311931 + -0.5 = -4.653311931
x = -4.653311931

Simplifying
x = -4.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.653311931, -4.653311931}
Solution
x = {3.653311931, -4.653311931}

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