x^2-11x-196=0

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Solution for x^2-11x-196=0 equation:


Simplifying
x2 + -11x + -196 = 0

Reorder the terms:
-196 + -11x + x2 = 0

Solving
-196 + -11x + 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 + -11x + 196 + x2 = 0 + 196

Reorder the terms:
-196 + 196 + -11x + x2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + -11x + x2 = 0 + 196
-11x + x2 = 0 + 196

Combine like terms: 0 + 196 = 196
-11x + x2 = 196

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 196 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 196 + 30.25

Combine like terms: 196 + 30.25 = 226.25
30.25 + -11x + x2 = 226.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 226.25

Calculate the square root of the right side: 15.041608956

Break this problem into two subproblems by setting 
(x + -5.5) equal to 15.041608956 and -15.041608956.

Subproblem 1

x + -5.5 = 15.041608956 Simplifying x + -5.5 = 15.041608956 Reorder the terms: -5.5 + x = 15.041608956 Solving -5.5 + x = 15.041608956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 15.041608956 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 15.041608956 + 5.5 x = 15.041608956 + 5.5 Combine like terms: 15.041608956 + 5.5 = 20.541608956 x = 20.541608956 Simplifying x = 20.541608956

Subproblem 2

x + -5.5 = -15.041608956 Simplifying x + -5.5 = -15.041608956 Reorder the terms: -5.5 + x = -15.041608956 Solving -5.5 + x = -15.041608956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -15.041608956 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -15.041608956 + 5.5 x = -15.041608956 + 5.5 Combine like terms: -15.041608956 + 5.5 = -9.541608956 x = -9.541608956 Simplifying x = -9.541608956

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.541608956, -9.541608956}

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