4x(x+14)=14

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Solution for 4x(x+14)=14 equation: 


Simplifying
4x(x + 14) = 14

Reorder the terms:
4x(14 + x) = 14
(14 * 4x + x * 4x) = 14
(56x + 4x2) = 14

Solving
56x + 4x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 56x + 4x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 28x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 28x + 2x2)' equal to zero and attempt to solve:

Simplifying
-7 + 28x + 2x2 = 0

Solving
-7 + 28x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + 14x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 14x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 14x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 14x + x2 = 0 + 3.5
14x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
14x + x2 = 3.5

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 3.5 + 49

Reorder the terms:
49 + 14x + x2 = 3.5 + 49

Combine like terms: 3.5 + 49 = 52.5
49 + 14x + x2 = 52.5

Factor a perfect square on the left side:
(x + 7)(x + 7) = 52.5

Calculate the square root of the right side: 7.245688373

Break this problem into two subproblems by setting 
(x + 7) equal to 7.245688373 and -7.245688373.


Subproblem 1
x + 7 = 7.245688373

Simplifying
x + 7 = 7.245688373

Reorder the terms:
7 + x = 7.245688373

Solving
7 + x = 7.245688373

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 7.245688373 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.245688373 + -7
x = 7.245688373 + -7

Combine like terms: 7.245688373 + -7 = 0.245688373
x = 0.245688373

Simplifying
x = 0.245688373


Subproblem 2
x + 7 = -7.245688373

Simplifying
x + 7 = -7.245688373

Reorder the terms:
7 + x = -7.245688373

Solving
7 + x = -7.245688373

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -7.245688373 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.245688373 + -7
x = -7.245688373 + -7

Combine like terms: -7.245688373 + -7 = -14.245688373
x = -14.245688373

Simplifying
x = -14.245688373


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.245688373, -14.245688373}
Solution
x = {0.245688373, -14.245688373}

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