2x+34=4x(x+5)

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Solution for 2x+34=4x(x+5) equation: 


Simplifying
2x + 34 = 4x(x + 5)

Reorder the terms:
34 + 2x = 4x(x + 5)

Reorder the terms:
34 + 2x = 4x(5 + x)
34 + 2x = (5 * 4x + x * 4x)
34 + 2x = (20x + 4x2)

Solving
34 + 2x = 20x + 4x2

Solving for variable 'x'.

Combine like terms: 2x + -20x = -18x
34 + -18x + -4x2 = 20x + 4x2 + -20x + -4x2

Reorder the terms:
34 + -18x + -4x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
34 + -18x + -4x2 = 0 + 4x2 + -4x2
34 + -18x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
34 + -18x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -9x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + -9x + -2x2)' equal to zero and attempt to solve:

Simplifying
17 + -9x + -2x2 = 0

Solving
17 + -9x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-8.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 4.5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 4.5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 4.5x + x2 = 0 + 8.5
4.5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
4.5x + x2 = 8.5

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 8.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 8.5 + 5.0625

Combine like terms: 8.5 + 5.0625 = 13.5625
5.0625 + 4.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + 2.25) equal to 3.682729966 and -3.682729966.


Subproblem 1
x + 2.25 = 3.682729966

Simplifying
x + 2.25 = 3.682729966

Reorder the terms:
2.25 + x = 3.682729966

Solving
2.25 + x = 3.682729966

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 3.682729966 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 3.682729966 + -2.25
x = 3.682729966 + -2.25

Combine like terms: 3.682729966 + -2.25 = 1.432729966
x = 1.432729966

Simplifying
x = 1.432729966


Subproblem 2
x + 2.25 = -3.682729966

Simplifying
x + 2.25 = -3.682729966

Reorder the terms:
2.25 + x = -3.682729966

Solving
2.25 + x = -3.682729966

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -3.682729966 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -3.682729966 + -2.25
x = -3.682729966 + -2.25

Combine like terms: -3.682729966 + -2.25 = -5.932729966
x = -5.932729966

Simplifying
x = -5.932729966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.432729966, -5.932729966}
Solution
x = {1.432729966, -5.932729966}

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