x^2-35x+190=0

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Solution for x^2-35x+190=0 equation: 


Simplifying
x2 + -35x + 190 = 0

Reorder the terms:
190 + -35x + x2 = 0

Solving
190 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-190' to each side of the equation.
190 + -35x + -190 + x2 = 0 + -190

Reorder the terms:
190 + -190 + -35x + x2 = 0 + -190

Combine like terms: 190 + -190 = 0
0 + -35x + x2 = 0 + -190
-35x + x2 = 0 + -190

Combine like terms: 0 + -190 = -190
-35x + x2 = -190

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -190 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -190 + 306.25

Combine like terms: -190 + 306.25 = 116.25
306.25 + -35x + x2 = 116.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 116.25

Calculate the square root of the right side: 10.781929326

Break this problem into two subproblems by setting 
(x + -17.5) equal to 10.781929326 and -10.781929326.


Subproblem 1
x + -17.5 = 10.781929326

Simplifying
x + -17.5 = 10.781929326

Reorder the terms:
-17.5 + x = 10.781929326

Solving
-17.5 + x = 10.781929326

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 10.781929326 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 10.781929326 + 17.5
x = 10.781929326 + 17.5

Combine like terms: 10.781929326 + 17.5 = 28.281929326
x = 28.281929326

Simplifying
x = 28.281929326


Subproblem 2
x + -17.5 = -10.781929326

Simplifying
x + -17.5 = -10.781929326

Reorder the terms:
-17.5 + x = -10.781929326

Solving
-17.5 + x = -10.781929326

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -10.781929326 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -10.781929326 + 17.5
x = -10.781929326 + 17.5

Combine like terms: -10.781929326 + 17.5 = 6.718070674
x = 6.718070674

Simplifying
x = 6.718070674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.281929326, 6.718070674}

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