x^2-5x-196=0

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Solution for x^2-5x-196=0 equation: 


Simplifying
x2 + -5x + -196 = 0

Reorder the terms:
-196 + -5x + x2 = 0

Solving
-196 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '196' to each side of the equation.
-196 + -5x + 196 + x2 = 0 + 196

Reorder the terms:
-196 + 196 + -5x + x2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + -5x + x2 = 0 + 196
-5x + x2 = 0 + 196

Combine like terms: 0 + 196 = 196
-5x + x2 = 196

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 196 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 196 + 6.25

Combine like terms: 196 + 6.25 = 202.25
6.25 + -5x + x2 = 202.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(x + -2.5) equal to 14.221462653 and -14.221462653.


Subproblem 1
x + -2.5 = 14.221462653

Simplifying
x + -2.5 = 14.221462653

Reorder the terms:
-2.5 + x = 14.221462653

Solving
-2.5 + x = 14.221462653

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 14.221462653 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 14.221462653 + 2.5
x = 14.221462653 + 2.5

Combine like terms: 14.221462653 + 2.5 = 16.721462653
x = 16.721462653

Simplifying
x = 16.721462653


Subproblem 2
x + -2.5 = -14.221462653

Simplifying
x + -2.5 = -14.221462653

Reorder the terms:
-2.5 + x = -14.221462653

Solving
-2.5 + x = -14.221462653

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -14.221462653 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -14.221462653 + 2.5
x = -14.221462653 + 2.5

Combine like terms: -14.221462653 + 2.5 = -11.721462653
x = -11.721462653

Simplifying
x = -11.721462653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.721462653, -11.721462653}

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