x^2-97-20x=0

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Solution for x^2-97-20x=0 equation: 


Simplifying
x2 + -97 + -20x = 0

Reorder the terms:
-97 + -20x + x2 = 0

Solving
-97 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '97' to each side of the equation.
-97 + -20x + 97 + x2 = 0 + 97

Reorder the terms:
-97 + 97 + -20x + x2 = 0 + 97

Combine like terms: -97 + 97 = 0
0 + -20x + x2 = 0 + 97
-20x + x2 = 0 + 97

Combine like terms: 0 + 97 = 97
-20x + x2 = 97

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 = 97 + 100

Reorder the terms:
100 + -20x + x2 = 97 + 100

Combine like terms: 97 + 100 = 197
100 + -20x + x2 = 197

Factor a perfect square on the left side:
(x + -10)(x + -10) = 197

Calculate the square root of the right side: 14.035668848

Break this problem into two subproblems by setting 
(x + -10) equal to 14.035668848 and -14.035668848.


Subproblem 1
x + -10 = 14.035668848

Simplifying
x + -10 = 14.035668848

Reorder the terms:
-10 + x = 14.035668848

Solving
-10 + x = 14.035668848

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 = 14.035668848 + 10

Combine like terms: -10 + 10 = 0
0 + x = 14.035668848 + 10
x = 14.035668848 + 10

Combine like terms: 14.035668848 + 10 = 24.035668848
x = 24.035668848

Simplifying
x = 24.035668848


Subproblem 2
x + -10 = -14.035668848

Simplifying
x + -10 = -14.035668848

Reorder the terms:
-10 + x = -14.035668848

Solving
-10 + x = -14.035668848

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 = -14.035668848 + 10

Combine like terms: -10 + 10 = 0
0 + x = -14.035668848 + 10
x = -14.035668848 + 10

Combine like terms: -14.035668848 + 10 = -4.035668848
x = -4.035668848

Simplifying
x = -4.035668848


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.035668848, -4.035668848}

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