x^2-28x+48=0

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Solution for x^2-28x+48=0 equation: 


Simplifying
x2 + -28x + 48 = 0

Reorder the terms:
48 + -28x + x2 = 0

Solving
48 + -28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + -28x + -48 + x2 = 0 + -48

Reorder the terms:
48 + -48 + -28x + x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -28x + x2 = 0 + -48
-28x + x2 = 0 + -48

Combine like terms: 0 + -48 = -48
-28x + x2 = -48

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = -48 + 196

Reorder the terms:
196 + -28x + x2 = -48 + 196

Combine like terms: -48 + 196 = 148
196 + -28x + x2 = 148

Factor a perfect square on the left side:
(x + -14)(x + -14) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + -14) equal to 12.165525061 and -12.165525061.


Subproblem 1
x + -14 = 12.165525061

Simplifying
x + -14 = 12.165525061

Reorder the terms:
-14 + x = 12.165525061

Solving
-14 + x = 12.165525061

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + x = 12.165525061 + 14

Combine like terms: -14 + 14 = 0
0 + x = 12.165525061 + 14
x = 12.165525061 + 14

Combine like terms: 12.165525061 + 14 = 26.165525061
x = 26.165525061

Simplifying
x = 26.165525061


Subproblem 2
x + -14 = -12.165525061

Simplifying
x + -14 = -12.165525061

Reorder the terms:
-14 + x = -12.165525061

Solving
-14 + x = -12.165525061

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + x = -12.165525061 + 14

Combine like terms: -14 + 14 = 0
0 + x = -12.165525061 + 14
x = -12.165525061 + 14

Combine like terms: -12.165525061 + 14 = 1.834474939
x = 1.834474939

Simplifying
x = 1.834474939


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.165525061, 1.834474939}

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