x^2-89x+1=0

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Solution for x^2-89x+1=0 equation: 


Simplifying
x2 + -89x + 1 = 0

Reorder the terms:
1 + -89x + x2 = 0

Solving
1 + -89x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -89x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -89x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -89x + x2 = 0 + -1
-89x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-89x + x2 = -1

The x term is -89x.  Take half its coefficient (-44.5).
Square it (1980.25) and add it to both sides.

Add '1980.25' to each side of the equation.
-89x + 1980.25 + x2 = -1 + 1980.25

Reorder the terms:
1980.25 + -89x + x2 = -1 + 1980.25

Combine like terms: -1 + 1980.25 = 1979.25
1980.25 + -89x + x2 = 1979.25

Factor a perfect square on the left side:
(x + -44.5)(x + -44.5) = 1979.25

Calculate the square root of the right side: 44.488762626

Break this problem into two subproblems by setting 
(x + -44.5) equal to 44.488762626 and -44.488762626.


Subproblem 1
x + -44.5 = 44.488762626

Simplifying
x + -44.5 = 44.488762626

Reorder the terms:
-44.5 + x = 44.488762626

Solving
-44.5 + x = 44.488762626

Solving for variable 'x'.

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

Add '44.5' to each side of the equation.
-44.5 + 44.5 + x = 44.488762626 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + x = 44.488762626 + 44.5
x = 44.488762626 + 44.5

Combine like terms: 44.488762626 + 44.5 = 88.988762626
x = 88.988762626

Simplifying
x = 88.988762626


Subproblem 2
x + -44.5 = -44.488762626

Simplifying
x + -44.5 = -44.488762626

Reorder the terms:
-44.5 + x = -44.488762626

Solving
-44.5 + x = -44.488762626

Solving for variable 'x'.

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

Add '44.5' to each side of the equation.
-44.5 + 44.5 + x = -44.488762626 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + x = -44.488762626 + 44.5
x = -44.488762626 + 44.5

Combine like terms: -44.488762626 + 44.5 = 0.011237374
x = 0.011237374

Simplifying
x = 0.011237374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {88.988762626, 0.011237374}

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