2x^2-350x+350=0

Solution for 2x^2-350x+350=0 equation:

Simplifying
2x2 + -350x + 350 = 0

Reorder the terms:
350 + -350x + 2x2 = 0

Solving
350 + -350x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(175 + -175x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(175 + -175x + x2)' equal to zero and attempt to solve:

Simplifying
175 + -175x + x2 = 0

Solving
175 + -175x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-175' to each side of the equation.
175 + -175x + -175 + x2 = 0 + -175

Reorder the terms:
175 + -175 + -175x + x2 = 0 + -175

Combine like terms: 175 + -175 = 0
0 + -175x + x2 = 0 + -175
-175x + x2 = 0 + -175

Combine like terms: 0 + -175 = -175
-175x + x2 = -175

The x term is -175x.  Take half its coefficient (-87.5).
Square it (7656.25) and add it to both sides.

Add '7656.25' to each side of the equation.
-175x + 7656.25 + x2 = -175 + 7656.25

Reorder the terms:
7656.25 + -175x + x2 = -175 + 7656.25

Combine like terms: -175 + 7656.25 = 7481.25
7656.25 + -175x + x2 = 7481.25

Factor a perfect square on the left side:
(x + -87.5)(x + -87.5) = 7481.25

Calculate the square root of the right side: 86.49421946

Break this problem into two subproblems by setting 
(x + -87.5) equal to 86.49421946 and -86.49421946.

Subproblem 1
x + -87.5 = 86.49421946

Simplifying
x + -87.5 = 86.49421946

Reorder the terms:
-87.5 + x = 86.49421946

Solving
-87.5 + x = 86.49421946

Solving for variable 'x'.

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

Add '87.5' to each side of the equation.
-87.5 + 87.5 + x = 86.49421946 + 87.5

Combine like terms: -87.5 + 87.5 = 0.0
0.0 + x = 86.49421946 + 87.5
x = 86.49421946 + 87.5

Combine like terms: 86.49421946 + 87.5 = 173.99421946
x = 173.99421946

Simplifying
x = 173.99421946

Subproblem 2
x + -87.5 = -86.49421946

Simplifying
x + -87.5 = -86.49421946

Reorder the terms:
-87.5 + x = -86.49421946

Solving
-87.5 + x = -86.49421946

Solving for variable 'x'.

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

Add '87.5' to each side of the equation.
-87.5 + 87.5 + x = -86.49421946 + 87.5

Combine like terms: -87.5 + 87.5 = 0.0
0.0 + x = -86.49421946 + 87.5
x = -86.49421946 + 87.5

Combine like terms: -86.49421946 + 87.5 = 1.00578054
x = 1.00578054

Simplifying
x = 1.00578054

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {173.99421946, 1.00578054}
Solution
x = {173.99421946, 1.00578054}