-7x^2-45x+35=0

Solution for -7x^2-45x+35=0 equation:

Simplifying
-7x2 + -45x + 35 = 0

Reorder the terms:
35 + -45x + -7x2 = 0

Solving
35 + -45x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-5 + 6.428571429x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6.428571429x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 6.428571429x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6.428571429x + x2 = 0 + 5
6.428571429x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
6.428571429x + x2 = 5

The x term is 6.428571429x.  Take half its coefficient (3.214285715).
Square it (10.33163266) and add it to both sides.

Add '10.33163266' to each side of the equation.
6.428571429x + 10.33163266 + x2 = 5 + 10.33163266

Reorder the terms:
10.33163266 + 6.428571429x + x2 = 5 + 10.33163266

Combine like terms: 5 + 10.33163266 = 15.33163266
10.33163266 + 6.428571429x + x2 = 15.33163266

Factor a perfect square on the left side:
(x + 3.214285715)(x + 3.214285715) = 15.33163266

Calculate the square root of the right side: 3.915562879

Break this problem into two subproblems by setting 
(x + 3.214285715) equal to 3.915562879 and -3.915562879.

Subproblem 1
x + 3.214285715 = 3.915562879

Simplifying
x + 3.214285715 = 3.915562879

Reorder the terms:
3.214285715 + x = 3.915562879

Solving
3.214285715 + x = 3.915562879

Solving for variable 'x'.

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

Add '-3.214285715' to each side of the equation.
3.214285715 + -3.214285715 + x = 3.915562879 + -3.214285715

Combine like terms: 3.214285715 + -3.214285715 = 0.000000000
0.000000000 + x = 3.915562879 + -3.214285715
x = 3.915562879 + -3.214285715

Combine like terms: 3.915562879 + -3.214285715 = 0.701277164
x = 0.701277164

Simplifying
x = 0.701277164

Subproblem 2
x + 3.214285715 = -3.915562879

Simplifying
x + 3.214285715 = -3.915562879

Reorder the terms:
3.214285715 + x = -3.915562879

Solving
3.214285715 + x = -3.915562879

Solving for variable 'x'.

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

Add '-3.214285715' to each side of the equation.
3.214285715 + -3.214285715 + x = -3.915562879 + -3.214285715

Combine like terms: 3.214285715 + -3.214285715 = 0.000000000
0.000000000 + x = -3.915562879 + -3.214285715
x = -3.915562879 + -3.214285715

Combine like terms: -3.915562879 + -3.214285715 = -7.129848594
x = -7.129848594

Simplifying
x = -7.129848594

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.701277164, -7.129848594}