x^2-48x+25=0

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Solution for x^2-48x+25=0 equation: 


Simplifying
x2 + -48x + 25 = 0

Reorder the terms:
25 + -48x + x2 = 0

Solving
25 + -48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -48x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -48x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -48x + x2 = 0 + -25
-48x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-48x + x2 = -25

The x term is -48x.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48x + 576 + x2 = -25 + 576

Reorder the terms:
576 + -48x + x2 = -25 + 576

Combine like terms: -25 + 576 = 551
576 + -48x + x2 = 551

Factor a perfect square on the left side:
(x + -24)(x + -24) = 551

Calculate the square root of the right side: 23.473389189

Break this problem into two subproblems by setting 
(x + -24) equal to 23.473389189 and -23.473389189.


Subproblem 1
x + -24 = 23.473389189

Simplifying
x + -24 = 23.473389189

Reorder the terms:
-24 + x = 23.473389189

Solving
-24 + x = 23.473389189

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = 23.473389189 + 24

Combine like terms: -24 + 24 = 0
0 + x = 23.473389189 + 24
x = 23.473389189 + 24

Combine like terms: 23.473389189 + 24 = 47.473389189
x = 47.473389189

Simplifying
x = 47.473389189


Subproblem 2
x + -24 = -23.473389189

Simplifying
x + -24 = -23.473389189

Reorder the terms:
-24 + x = -23.473389189

Solving
-24 + x = -23.473389189

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = -23.473389189 + 24

Combine like terms: -24 + 24 = 0
0 + x = -23.473389189 + 24
x = -23.473389189 + 24

Combine like terms: -23.473389189 + 24 = 0.526610811
x = 0.526610811

Simplifying
x = 0.526610811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.473389189, 0.526610811}

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