x^2-35x+100=0

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Solution for x^2-35x+100=0 equation: 


Simplifying
x2 + -35x + 100 = 0

Reorder the terms:
100 + -35x + x2 = 0

Solving
100 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -35x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -35x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -35x + x2 = 0 + -100
-35x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-35x + x2 = -100

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 = -100 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -100 + 306.25

Combine like terms: -100 + 306.25 = 206.25
306.25 + -35x + x2 = 206.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(x + -17.5) equal to 14.361406616 and -14.361406616.


Subproblem 1
x + -17.5 = 14.361406616

Simplifying
x + -17.5 = 14.361406616

Reorder the terms:
-17.5 + x = 14.361406616

Solving
-17.5 + x = 14.361406616

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 = 14.361406616 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 14.361406616 + 17.5
x = 14.361406616 + 17.5

Combine like terms: 14.361406616 + 17.5 = 31.861406616
x = 31.861406616

Simplifying
x = 31.861406616


Subproblem 2
x + -17.5 = -14.361406616

Simplifying
x + -17.5 = -14.361406616

Reorder the terms:
-17.5 + x = -14.361406616

Solving
-17.5 + x = -14.361406616

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 = -14.361406616 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -14.361406616 + 17.5
x = -14.361406616 + 17.5

Combine like terms: -14.361406616 + 17.5 = 3.138593384
x = 3.138593384

Simplifying
x = 3.138593384


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.861406616, 3.138593384}

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