2x^2+28x+1=0

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Solution for 2x^2+28x+1=0 equation: 


Simplifying
2x2 + 28x + 1 = 0

Reorder the terms:
1 + 28x + 2x2 = 0

Solving
1 + 28x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
0.5 + 14x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 14x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 14x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 14x + x2 = 0 + -0.5
14x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
14x + x2 = -0.5

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 = -0.5 + 49

Reorder the terms:
49 + 14x + x2 = -0.5 + 49

Combine like terms: -0.5 + 49 = 48.5
49 + 14x + x2 = 48.5

Factor a perfect square on the left side:
(x + 7)(x + 7) = 48.5

Calculate the square root of the right side: 6.964194139

Break this problem into two subproblems by setting 
(x + 7) equal to 6.964194139 and -6.964194139.


Subproblem 1
x + 7 = 6.964194139

Simplifying
x + 7 = 6.964194139

Reorder the terms:
7 + x = 6.964194139

Solving
7 + x = 6.964194139

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 = 6.964194139 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.964194139 + -7
x = 6.964194139 + -7

Combine like terms: 6.964194139 + -7 = -0.035805861
x = -0.035805861

Simplifying
x = -0.035805861


Subproblem 2
x + 7 = -6.964194139

Simplifying
x + 7 = -6.964194139

Reorder the terms:
7 + x = -6.964194139

Solving
7 + x = -6.964194139

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 = -6.964194139 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.964194139 + -7
x = -6.964194139 + -7

Combine like terms: -6.964194139 + -7 = -13.964194139
x = -13.964194139

Simplifying
x = -13.964194139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.035805861, -13.964194139}

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