7x^2+14x+35=3815

Solution for 7x^2+14x+35=3815 equation:

Simplifying
7x2 + 14x + 35 = 3815

Reorder the terms:
35 + 14x + 7x2 = 3815

Solving
35 + 14x + 7x2 = 3815

Solving for variable 'x'.

Reorder the terms:
35 + -3815 + 14x + 7x2 = 3815 + -3815

Combine like terms: 35 + -3815 = -3780
-3780 + 14x + 7x2 = 3815 + -3815

Combine like terms: 3815 + -3815 = 0
-3780 + 14x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-540 + 2x + x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-540 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-540 + 2x + x2 = 0

Solving
-540 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '540' to each side of the equation.
-540 + 2x + 540 + x2 = 0 + 540

Reorder the terms:
-540 + 540 + 2x + x2 = 0 + 540

Combine like terms: -540 + 540 = 0
0 + 2x + x2 = 0 + 540
2x + x2 = 0 + 540

Combine like terms: 0 + 540 = 540
2x + x2 = 540

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 540 + 1

Reorder the terms:
1 + 2x + x2 = 540 + 1

Combine like terms: 540 + 1 = 541
1 + 2x + x2 = 541

Factor a perfect square on the left side:
(x + 1)(x + 1) = 541

Calculate the square root of the right side: 23.259406699

Break this problem into two subproblems by setting 
(x + 1) equal to 23.259406699 and -23.259406699.

Subproblem 1
x + 1 = 23.259406699

Simplifying
x + 1 = 23.259406699

Reorder the terms:
1 + x = 23.259406699

Solving
1 + x = 23.259406699

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 23.259406699 + -1

Combine like terms: 1 + -1 = 0
0 + x = 23.259406699 + -1
x = 23.259406699 + -1

Combine like terms: 23.259406699 + -1 = 22.259406699
x = 22.259406699

Simplifying
x = 22.259406699

Subproblem 2
x + 1 = -23.259406699

Simplifying
x + 1 = -23.259406699

Reorder the terms:
1 + x = -23.259406699

Solving
1 + x = -23.259406699

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -23.259406699 + -1

Combine like terms: 1 + -1 = 0
0 + x = -23.259406699 + -1
x = -23.259406699 + -1

Combine like terms: -23.259406699 + -1 = -24.259406699
x = -24.259406699

Simplifying
x = -24.259406699

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.259406699, -24.259406699}
Solution
x = {22.259406699, -24.259406699}