x^2-25x-11=0

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Solution for x^2-25x-11=0 equation: 


Simplifying
x2 + -25x + -11 = 0

Reorder the terms:
-11 + -25x + x2 = 0

Solving
-11 + -25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -25x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -25x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -25x + x2 = 0 + 11
-25x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-25x + x2 = 11

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = 11 + 156.25

Reorder the terms:
156.25 + -25x + x2 = 11 + 156.25

Combine like terms: 11 + 156.25 = 167.25
156.25 + -25x + x2 = 167.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 167.25

Calculate the square root of the right side: 12.932517156

Break this problem into two subproblems by setting 
(x + -12.5) equal to 12.932517156 and -12.932517156.


Subproblem 1
x + -12.5 = 12.932517156

Simplifying
x + -12.5 = 12.932517156

Reorder the terms:
-12.5 + x = 12.932517156

Solving
-12.5 + x = 12.932517156

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 12.932517156 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 12.932517156 + 12.5
x = 12.932517156 + 12.5

Combine like terms: 12.932517156 + 12.5 = 25.432517156
x = 25.432517156

Simplifying
x = 25.432517156


Subproblem 2
x + -12.5 = -12.932517156

Simplifying
x + -12.5 = -12.932517156

Reorder the terms:
-12.5 + x = -12.932517156

Solving
-12.5 + x = -12.932517156

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -12.932517156 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -12.932517156 + 12.5
x = -12.932517156 + 12.5

Combine like terms: -12.932517156 + 12.5 = -0.432517156
x = -0.432517156

Simplifying
x = -0.432517156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.432517156, -0.432517156}

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