10x^2+38x+35=0

Solution for 10x^2+38x+35=0 equation:

Simplifying
10x2 + 38x + 35 = 0

Reorder the terms:
35 + 38x + 10x2 = 0

Solving
35 + 38x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
3.5 + 3.8x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 3.8x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 3.8x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 3.8x + x2 = 0 + -3.5
3.8x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
3.8x + x2 = -3.5

The x term is 3.8x.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8x + 3.61 + x2 = -3.5 + 3.61

Reorder the terms:
3.61 + 3.8x + x2 = -3.5 + 3.61

Combine like terms: -3.5 + 3.61 = 0.11
3.61 + 3.8x + x2 = 0.11

Factor a perfect square on the left side:
(x + 1.9)(x + 1.9) = 0.11

Calculate the square root of the right side: 0.331662479

Break this problem into two subproblems by setting 
(x + 1.9) equal to 0.331662479 and -0.331662479.

Subproblem 1
x + 1.9 = 0.331662479

Simplifying
x + 1.9 = 0.331662479

Reorder the terms:
1.9 + x = 0.331662479

Solving
1.9 + x = 0.331662479

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = 0.331662479 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = 0.331662479 + -1.9
x = 0.331662479 + -1.9

Combine like terms: 0.331662479 + -1.9 = -1.568337521
x = -1.568337521

Simplifying
x = -1.568337521

Subproblem 2
x + 1.9 = -0.331662479

Simplifying
x + 1.9 = -0.331662479

Reorder the terms:
1.9 + x = -0.331662479

Solving
1.9 + x = -0.331662479

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = -0.331662479 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = -0.331662479 + -1.9
x = -0.331662479 + -1.9

Combine like terms: -0.331662479 + -1.9 = -2.231662479
x = -2.231662479

Simplifying
x = -2.231662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.568337521, -2.231662479}