x^2-25x+13=0

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Solution for x^2-25x+13=0 equation:


Simplifying
x2 + -25x + 13 = 0

Reorder the terms:
13 + -25x + x2 = 0

Solving
13 + -25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -25x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -25x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -25x + x2 = 0 + -13
-25x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-25x + x2 = -13

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 = -13 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -13 + 156.25

Combine like terms: -13 + 156.25 = 143.25
156.25 + -25x + x2 = 143.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 143.25

Calculate the square root of the right side: 11.968709204

Break this problem into two subproblems by setting 
(x + -12.5) equal to 11.968709204 and -11.968709204.


Subproblem 1
x + -12.5 = 11.968709204

Simplifying
x + -12.5 = 11.968709204

Reorder the terms:
-12.5 + x = 11.968709204

Solving
-12.5 + x = 11.968709204

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 = 11.968709204 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 11.968709204 + 12.5
x = 11.968709204 + 12.5

Combine like terms: 11.968709204 + 12.5 = 24.468709204
x = 24.468709204

Simplifying
x = 24.468709204


Subproblem 2
x + -12.5 = -11.968709204

Simplifying
x + -12.5 = -11.968709204

Reorder the terms:
-12.5 + x = -11.968709204

Solving
-12.5 + x = -11.968709204

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 = -11.968709204 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -11.968709204 + 12.5
x = -11.968709204 + 12.5

Combine like terms: -11.968709204 + 12.5 = 0.531290796
x = 0.531290796

Simplifying
x = 0.531290796


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.468709204, 0.531290796}

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