5x^2+6x+1=42

Solution for 5x^2+6x+1=42 equation:

Simplifying
5x2 + 6x + 1 = 42

Reorder the terms:
1 + 6x + 5x2 = 42

Solving
1 + 6x + 5x2 = 42

Solving for variable 'x'.

Reorder the terms:
1 + -42 + 6x + 5x2 = 42 + -42

Combine like terms: 1 + -42 = -41
-41 + 6x + 5x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-41 + 6x + 5x2 = 0

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

Divide each side by '5'.
-8.2 + 1.2x + x2 = 0

Move the constant term to the right:

Add '8.2' to each side of the equation.
-8.2 + 1.2x + 8.2 + x2 = 0 + 8.2

Reorder the terms:
-8.2 + 8.2 + 1.2x + x2 = 0 + 8.2

Combine like terms: -8.2 + 8.2 = 0.0
0.0 + 1.2x + x2 = 0 + 8.2
1.2x + x2 = 0 + 8.2

Combine like terms: 0 + 8.2 = 8.2
1.2x + x2 = 8.2

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 8.2 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 8.2 + 0.36

Combine like terms: 8.2 + 0.36 = 8.56
0.36 + 1.2x + x2 = 8.56

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 8.56

Calculate the square root of the right side: 2.925747768

Break this problem into two subproblems by setting 
(x + 0.6) equal to 2.925747768 and -2.925747768.

Subproblem 1
x + 0.6 = 2.925747768

Simplifying
x + 0.6 = 2.925747768

Reorder the terms:
0.6 + x = 2.925747768

Solving
0.6 + x = 2.925747768

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = 2.925747768 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = 2.925747768 + -0.6
x = 2.925747768 + -0.6

Combine like terms: 2.925747768 + -0.6 = 2.325747768
x = 2.325747768

Simplifying
x = 2.325747768

Subproblem 2
x + 0.6 = -2.925747768

Simplifying
x + 0.6 = -2.925747768

Reorder the terms:
0.6 + x = -2.925747768

Solving
0.6 + x = -2.925747768

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = -2.925747768 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = -2.925747768 + -0.6
x = -2.925747768 + -0.6

Combine like terms: -2.925747768 + -0.6 = -3.525747768
x = -3.525747768

Simplifying
x = -3.525747768

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.325747768, -3.525747768}