14x(4x+2)=40

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Solution for 14x(4x+2)=40 equation: 


Simplifying
14x(4x + 2) = 40

Reorder the terms:
14x(2 + 4x) = 40
(2 * 14x + 4x * 14x) = 40
(28x + 56x2) = 40

Solving
28x + 56x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 28x + 56x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 28x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 7x + 14x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + 7x + 14x2)' equal to zero and attempt to solve:

Simplifying
-10 + 7x + 14x2 = 0

Solving
-10 + 7x + 14x2 = 0

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

Divide each side by '14'.
-0.7142857143 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 0.5x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 0.5x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 0.5x + x2 = 0 + 0.7142857143
0.5x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
0.5x + x2 = 0.7142857143

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.7142857143 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.7142857143 + 0.0625

Combine like terms: 0.7142857143 + 0.0625 = 0.7767857143
0.0625 + 0.5x + x2 = 0.7767857143

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.7767857143

Calculate the square root of the right side: 0.881354477

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.881354477 and -0.881354477.


Subproblem 1
x + 0.25 = 0.881354477

Simplifying
x + 0.25 = 0.881354477

Reorder the terms:
0.25 + x = 0.881354477

Solving
0.25 + x = 0.881354477

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.881354477 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.881354477 + -0.25
x = 0.881354477 + -0.25

Combine like terms: 0.881354477 + -0.25 = 0.631354477
x = 0.631354477

Simplifying
x = 0.631354477


Subproblem 2
x + 0.25 = -0.881354477

Simplifying
x + 0.25 = -0.881354477

Reorder the terms:
0.25 + x = -0.881354477

Solving
0.25 + x = -0.881354477

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.881354477 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.881354477 + -0.25
x = -0.881354477 + -0.25

Combine like terms: -0.881354477 + -0.25 = -1.131354477
x = -1.131354477

Simplifying
x = -1.131354477


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.631354477, -1.131354477}
Solution
x = {0.631354477, -1.131354477}

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