35x^2+42x+12=0

Solution for 35x^2+42x+12=0 equation:

Simplifying
35x2 + 42x + 12 = 0

Reorder the terms:
12 + 42x + 35x2 = 0

Solving
12 + 42x + 35x2 = 0

Solving for variable 'x'.

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

Divide each side by '35'.
0.3428571429 + 1.2x + x2 = 0

Move the constant term to the right:

Add '-0.3428571429' to each side of the equation.
0.3428571429 + 1.2x + -0.3428571429 + x2 = 0 + -0.3428571429

Reorder the terms:
0.3428571429 + -0.3428571429 + 1.2x + x2 = 0 + -0.3428571429

Combine like terms: 0.3428571429 + -0.3428571429 = 0.0000000000
0.0000000000 + 1.2x + x2 = 0 + -0.3428571429
1.2x + x2 = 0 + -0.3428571429

Combine like terms: 0 + -0.3428571429 = -0.3428571429
1.2x + x2 = -0.3428571429

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 = -0.3428571429 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = -0.3428571429 + 0.36

Combine like terms: -0.3428571429 + 0.36 = 0.0171428571
0.36 + 1.2x + x2 = 0.0171428571

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 0.0171428571

Calculate the square root of the right side: 0.130930734

Break this problem into two subproblems by setting 
(x + 0.6) equal to 0.130930734 and -0.130930734.

Subproblem 1
x + 0.6 = 0.130930734

Simplifying
x + 0.6 = 0.130930734

Reorder the terms:
0.6 + x = 0.130930734

Solving
0.6 + x = 0.130930734

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 = 0.130930734 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = 0.130930734 + -0.6
x = 0.130930734 + -0.6

Combine like terms: 0.130930734 + -0.6 = -0.469069266
x = -0.469069266

Simplifying
x = -0.469069266

Subproblem 2
x + 0.6 = -0.130930734

Simplifying
x + 0.6 = -0.130930734

Reorder the terms:
0.6 + x = -0.130930734

Solving
0.6 + x = -0.130930734

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 = -0.130930734 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = -0.130930734 + -0.6
x = -0.130930734 + -0.6

Combine like terms: -0.130930734 + -0.6 = -0.730930734
x = -0.730930734

Simplifying
x = -0.730930734

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.469069266, -0.730930734}