2x(2x+14)=50

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Solution for 2x(2x+14)=50 equation: 


Simplifying
2x(2x + 14) = 50

Reorder the terms:
2x(14 + 2x) = 50
(14 * 2x + 2x * 2x) = 50
(28x + 4x2) = 50

Solving
28x + 4x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + 28x + 4x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 14x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 14x + 2x2)' equal to zero and attempt to solve:

Simplifying
-25 + 14x + 2x2 = 0

Solving
-25 + 14x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + 7x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 7x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 7x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 7x + x2 = 0 + 12.5
7x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
7x + x2 = 12.5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 12.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 12.5 + 12.25

Combine like terms: 12.5 + 12.25 = 24.75
12.25 + 7x + x2 = 24.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 24.75

Calculate the square root of the right side: 4.974937186

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.974937186 and -4.974937186.


Subproblem 1
x + 3.5 = 4.974937186

Simplifying
x + 3.5 = 4.974937186

Reorder the terms:
3.5 + x = 4.974937186

Solving
3.5 + x = 4.974937186

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.974937186 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.974937186 + -3.5
x = 4.974937186 + -3.5

Combine like terms: 4.974937186 + -3.5 = 1.474937186
x = 1.474937186

Simplifying
x = 1.474937186


Subproblem 2
x + 3.5 = -4.974937186

Simplifying
x + 3.5 = -4.974937186

Reorder the terms:
3.5 + x = -4.974937186

Solving
3.5 + x = -4.974937186

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.974937186 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.974937186 + -3.5
x = -4.974937186 + -3.5

Combine like terms: -4.974937186 + -3.5 = -8.474937186
x = -8.474937186

Simplifying
x = -8.474937186


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.474937186, -8.474937186}
Solution
x = {1.474937186, -8.474937186}

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