2x^2+140x=7550

Solution for 2x^2+140x=7550 equation:

Simplifying
2x2 + 140x = 7550

Reorder the terms:
140x + 2x2 = 7550

Solving
140x + 2x2 = 7550

Solving for variable 'x'.

Reorder the terms:
-7550 + 140x + 2x2 = 7550 + -7550

Combine like terms: 7550 + -7550 = 0
-7550 + 140x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3775 + 70x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3775 + 70x + x2)' equal to zero and attempt to solve:

Simplifying
-3775 + 70x + x2 = 0

Solving
-3775 + 70x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3775' to each side of the equation.
-3775 + 70x + 3775 + x2 = 0 + 3775

Reorder the terms:
-3775 + 3775 + 70x + x2 = 0 + 3775

Combine like terms: -3775 + 3775 = 0
0 + 70x + x2 = 0 + 3775
70x + x2 = 0 + 3775

Combine like terms: 0 + 3775 = 3775
70x + x2 = 3775

The x term is 70x.  Take half its coefficient (35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
70x + 1225 + x2 = 3775 + 1225

Reorder the terms:
1225 + 70x + x2 = 3775 + 1225

Combine like terms: 3775 + 1225 = 5000
1225 + 70x + x2 = 5000

Factor a perfect square on the left side:
(x + 35)(x + 35) = 5000

Calculate the square root of the right side: 70.710678119

Break this problem into two subproblems by setting 
(x + 35) equal to 70.710678119 and -70.710678119.

Subproblem 1
x + 35 = 70.710678119

Simplifying
x + 35 = 70.710678119

Reorder the terms:
35 + x = 70.710678119

Solving
35 + x = 70.710678119

Solving for variable 'x'.

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

Add '-35' to each side of the equation.
35 + -35 + x = 70.710678119 + -35

Combine like terms: 35 + -35 = 0
0 + x = 70.710678119 + -35
x = 70.710678119 + -35

Combine like terms: 70.710678119 + -35 = 35.710678119
x = 35.710678119

Simplifying
x = 35.710678119

Subproblem 2
x + 35 = -70.710678119

Simplifying
x + 35 = -70.710678119

Reorder the terms:
35 + x = -70.710678119

Solving
35 + x = -70.710678119

Solving for variable 'x'.

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

Add '-35' to each side of the equation.
35 + -35 + x = -70.710678119 + -35

Combine like terms: 35 + -35 = 0
0 + x = -70.710678119 + -35
x = -70.710678119 + -35

Combine like terms: -70.710678119 + -35 = -105.710678119
x = -105.710678119

Simplifying
x = -105.710678119

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.710678119, -105.710678119}
Solution
x = {35.710678119, -105.710678119}