7x^2+8x+2=0

Solution for 7x^2+8x+2=0 equation:

Simplifying
7x2 + 8x + 2 = 0

Reorder the terms:
2 + 8x + 7x2 = 0

Solving
2 + 8x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
0.2857142857 + 1.142857143x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + 1.142857143x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + 1.142857143x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + 1.142857143x + x2 = 0 + -0.2857142857
1.142857143x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
1.142857143x + x2 = -0.2857142857

The x term is 1.142857143x.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143x + 0.3265306123 + x2 = -0.2857142857 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143x + x2 = -0.2857142857 + 0.3265306123

Combine like terms: -0.2857142857 + 0.3265306123 = 0.0408163266
0.3265306123 + 1.142857143x + x2 = 0.0408163266

Factor a perfect square on the left side:
(x + 0.5714285715)(x + 0.5714285715) = 0.0408163266

Calculate the square root of the right side: 0.202030509

Break this problem into two subproblems by setting 
(x + 0.5714285715) equal to 0.202030509 and -0.202030509.

Subproblem 1
x + 0.5714285715 = 0.202030509

Simplifying
x + 0.5714285715 = 0.202030509

Reorder the terms:
0.5714285715 + x = 0.202030509

Solving
0.5714285715 + x = 0.202030509

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = 0.202030509 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = 0.202030509 + -0.5714285715
x = 0.202030509 + -0.5714285715

Combine like terms: 0.202030509 + -0.5714285715 = -0.3693980625
x = -0.3693980625

Simplifying
x = -0.3693980625

Subproblem 2
x + 0.5714285715 = -0.202030509

Simplifying
x + 0.5714285715 = -0.202030509

Reorder the terms:
0.5714285715 + x = -0.202030509

Solving
0.5714285715 + x = -0.202030509

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = -0.202030509 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = -0.202030509 + -0.5714285715
x = -0.202030509 + -0.5714285715

Combine like terms: -0.202030509 + -0.5714285715 = -0.7734590805
x = -0.7734590805

Simplifying
x = -0.7734590805

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.3693980625, -0.7734590805}