x^2-20x+45=0

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Solution for x^2-20x+45=0 equation: 


Simplifying
x2 + -20x + 45 = 0

Reorder the terms:
45 + -20x + x2 = 0

Solving
45 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -20x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + -20x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -20x + x2 = 0 + -45
-20x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
-20x + x2 = -45

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -45 + 100

Reorder the terms:
100 + -20x + x2 = -45 + 100

Combine like terms: -45 + 100 = 55
100 + -20x + x2 = 55

Factor a perfect square on the left side:
(x + -10)(x + -10) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + -10) equal to 7.416198487 and -7.416198487.


Subproblem 1
x + -10 = 7.416198487

Simplifying
x + -10 = 7.416198487

Reorder the terms:
-10 + x = 7.416198487

Solving
-10 + x = 7.416198487

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 7.416198487 + 10

Combine like terms: -10 + 10 = 0
0 + x = 7.416198487 + 10
x = 7.416198487 + 10

Combine like terms: 7.416198487 + 10 = 17.416198487
x = 17.416198487

Simplifying
x = 17.416198487


Subproblem 2
x + -10 = -7.416198487

Simplifying
x + -10 = -7.416198487

Reorder the terms:
-10 + x = -7.416198487

Solving
-10 + x = -7.416198487

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -7.416198487 + 10

Combine like terms: -10 + 10 = 0
0 + x = -7.416198487 + 10
x = -7.416198487 + 10

Combine like terms: -7.416198487 + 10 = 2.583801513
x = 2.583801513

Simplifying
x = 2.583801513


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.416198487, 2.583801513}

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