19x^2+9x-35=0

Solution for 19x^2+9x-35=0 equation:

Simplifying
19x2 + 9x + -35 = 0

Reorder the terms:
-35 + 9x + 19x2 = 0

Solving
-35 + 9x + 19x2 = 0

Solving for variable 'x'.

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

Divide each side by '19'.
-1.842105263 + 0.4736842105x + x2 = 0

Move the constant term to the right:

Add '1.842105263' to each side of the equation.
-1.842105263 + 0.4736842105x + 1.842105263 + x2 = 0 + 1.842105263

Reorder the terms:
-1.842105263 + 1.842105263 + 0.4736842105x + x2 = 0 + 1.842105263

Combine like terms: -1.842105263 + 1.842105263 = 0.000000000
0.000000000 + 0.4736842105x + x2 = 0 + 1.842105263
0.4736842105x + x2 = 0 + 1.842105263

Combine like terms: 0 + 1.842105263 = 1.842105263
0.4736842105x + x2 = 1.842105263

The x term is 0.4736842105x.  Take half its coefficient (0.2368421053).
Square it (0.05609418284) and add it to both sides.

Add '0.05609418284' to each side of the equation.
0.4736842105x + 0.05609418284 + x2 = 1.842105263 + 0.05609418284

Reorder the terms:
0.05609418284 + 0.4736842105x + x2 = 1.842105263 + 0.05609418284

Combine like terms: 1.842105263 + 0.05609418284 = 1.89819944584
0.05609418284 + 0.4736842105x + x2 = 1.89819944584

Factor a perfect square on the left side:
(x + 0.2368421053)(x + 0.2368421053) = 1.89819944584

Calculate the square root of the right side: 1.377751591

Break this problem into two subproblems by setting 
(x + 0.2368421053) equal to 1.377751591 and -1.377751591.

Subproblem 1
x + 0.2368421053 = 1.377751591

Simplifying
x + 0.2368421053 = 1.377751591

Reorder the terms:
0.2368421053 + x = 1.377751591

Solving
0.2368421053 + x = 1.377751591

Solving for variable 'x'.

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

Add '-0.2368421053' to each side of the equation.
0.2368421053 + -0.2368421053 + x = 1.377751591 + -0.2368421053

Combine like terms: 0.2368421053 + -0.2368421053 = 0.0000000000
0.0000000000 + x = 1.377751591 + -0.2368421053
x = 1.377751591 + -0.2368421053

Combine like terms: 1.377751591 + -0.2368421053 = 1.1409094857
x = 1.1409094857

Simplifying
x = 1.1409094857

Subproblem 2
x + 0.2368421053 = -1.377751591

Simplifying
x + 0.2368421053 = -1.377751591

Reorder the terms:
0.2368421053 + x = -1.377751591

Solving
0.2368421053 + x = -1.377751591

Solving for variable 'x'.

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

Add '-0.2368421053' to each side of the equation.
0.2368421053 + -0.2368421053 + x = -1.377751591 + -0.2368421053

Combine like terms: 0.2368421053 + -0.2368421053 = 0.0000000000
0.0000000000 + x = -1.377751591 + -0.2368421053
x = -1.377751591 + -0.2368421053

Combine like terms: -1.377751591 + -0.2368421053 = -1.6145936963
x = -1.6145936963

Simplifying
x = -1.6145936963

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1409094857, -1.6145936963}