x^2-16x+24=0

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Solution for x^2-16x+24=0 equation: 


Simplifying
x2 + -16x + 24 = 0

Reorder the terms:
24 + -16x + x2 = 0

Solving
24 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -16x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -16x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -16x + x2 = 0 + -24
-16x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-16x + x2 = -24

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -24 + 64

Reorder the terms:
64 + -16x + x2 = -24 + 64

Combine like terms: -24 + 64 = 40
64 + -16x + x2 = 40

Factor a perfect square on the left side:
(x + -8)(x + -8) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -8) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -8 = 6.32455532

Simplifying
x + -8 = 6.32455532

Reorder the terms:
-8 + x = 6.32455532

Solving
-8 + x = 6.32455532

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 6.32455532 + 8

Combine like terms: -8 + 8 = 0
0 + x = 6.32455532 + 8
x = 6.32455532 + 8

Combine like terms: 6.32455532 + 8 = 14.32455532
x = 14.32455532

Simplifying
x = 14.32455532


Subproblem 2
x + -8 = -6.32455532

Simplifying
x + -8 = -6.32455532

Reorder the terms:
-8 + x = -6.32455532

Solving
-8 + x = -6.32455532

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -6.32455532 + 8

Combine like terms: -8 + 8 = 0
0 + x = -6.32455532 + 8
x = -6.32455532 + 8

Combine like terms: -6.32455532 + 8 = 1.67544468
x = 1.67544468

Simplifying
x = 1.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.32455532, 1.67544468}

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