x^2-24x+28=0

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Solution for x^2-24x+28=0 equation: 


Simplifying
x2 + -24x + 28 = 0

Reorder the terms:
28 + -24x + x2 = 0

Solving
28 + -24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -24x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -24x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -24x + x2 = 0 + -28
-24x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-24x + x2 = -28

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -28 + 144

Reorder the terms:
144 + -24x + x2 = -28 + 144

Combine like terms: -28 + 144 = 116
144 + -24x + x2 = 116

Factor a perfect square on the left side:
(x + -12)(x + -12) = 116

Calculate the square root of the right side: 10.770329614

Break this problem into two subproblems by setting 
(x + -12) equal to 10.770329614 and -10.770329614.


Subproblem 1
x + -12 = 10.770329614

Simplifying
x + -12 = 10.770329614

Reorder the terms:
-12 + x = 10.770329614

Solving
-12 + x = 10.770329614

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 10.770329614 + 12

Combine like terms: -12 + 12 = 0
0 + x = 10.770329614 + 12
x = 10.770329614 + 12

Combine like terms: 10.770329614 + 12 = 22.770329614
x = 22.770329614

Simplifying
x = 22.770329614


Subproblem 2
x + -12 = -10.770329614

Simplifying
x + -12 = -10.770329614

Reorder the terms:
-12 + x = -10.770329614

Solving
-12 + x = -10.770329614

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -10.770329614 + 12

Combine like terms: -12 + 12 = 0
0 + x = -10.770329614 + 12
x = -10.770329614 + 12

Combine like terms: -10.770329614 + 12 = 1.229670386
x = 1.229670386

Simplifying
x = 1.229670386


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.770329614, 1.229670386}

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