8x^2+35x-35=0

Solution for 8x^2+35x-35=0 equation:

Simplifying
8x2 + 35x + -35 = 0

Reorder the terms:
-35 + 35x + 8x2 = 0

Solving
-35 + 35x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-4.375 + 4.375x + x2 = 0

Move the constant term to the right:

Add '4.375' to each side of the equation.
-4.375 + 4.375x + 4.375 + x2 = 0 + 4.375

Reorder the terms:
-4.375 + 4.375 + 4.375x + x2 = 0 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + 4.375x + x2 = 0 + 4.375
4.375x + x2 = 0 + 4.375

Combine like terms: 0 + 4.375 = 4.375
4.375x + x2 = 4.375

The x term is 4.375x.  Take half its coefficient (2.1875).
Square it (4.78515625) and add it to both sides.

Add '4.78515625' to each side of the equation.
4.375x + 4.78515625 + x2 = 4.375 + 4.78515625

Reorder the terms:
4.78515625 + 4.375x + x2 = 4.375 + 4.78515625

Combine like terms: 4.375 + 4.78515625 = 9.16015625
4.78515625 + 4.375x + x2 = 9.16015625

Factor a perfect square on the left side:
(x + 2.1875)(x + 2.1875) = 9.16015625

Calculate the square root of the right side: 3.026575003

Break this problem into two subproblems by setting 
(x + 2.1875) equal to 3.026575003 and -3.026575003.

Subproblem 1
x + 2.1875 = 3.026575003

Simplifying
x + 2.1875 = 3.026575003

Reorder the terms:
2.1875 + x = 3.026575003

Solving
2.1875 + x = 3.026575003

Solving for variable 'x'.

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

Add '-2.1875' to each side of the equation.
2.1875 + -2.1875 + x = 3.026575003 + -2.1875

Combine like terms: 2.1875 + -2.1875 = 0.0000
0.0000 + x = 3.026575003 + -2.1875
x = 3.026575003 + -2.1875

Combine like terms: 3.026575003 + -2.1875 = 0.839075003
x = 0.839075003

Simplifying
x = 0.839075003

Subproblem 2
x + 2.1875 = -3.026575003

Simplifying
x + 2.1875 = -3.026575003

Reorder the terms:
2.1875 + x = -3.026575003

Solving
2.1875 + x = -3.026575003

Solving for variable 'x'.

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

Add '-2.1875' to each side of the equation.
2.1875 + -2.1875 + x = -3.026575003 + -2.1875

Combine like terms: 2.1875 + -2.1875 = 0.0000
0.0000 + x = -3.026575003 + -2.1875
x = -3.026575003 + -2.1875

Combine like terms: -3.026575003 + -2.1875 = -5.214075003
x = -5.214075003

Simplifying
x = -5.214075003

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.839075003, -5.214075003}