x^2-20x+24=0

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Solution for x^2-20x+24=0 equation: 


Simplifying
x2 + -20x + 24 = 0

Reorder the terms:
24 + -20x + x2 = 0

Solving
24 + -20x + 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 + -20x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -20x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -20x + x2 = 0 + -24
-20x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-20x + x2 = -24

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -24 + 100

Reorder the terms:
100 + -20x + x2 = -24 + 100

Combine like terms: -24 + 100 = 76
100 + -20x + x2 = 76

Factor a perfect square on the left side:
(x + -10)(x + -10) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + -10) equal to 8.717797887 and -8.717797887.


Subproblem 1
x + -10 = 8.717797887

Simplifying
x + -10 = 8.717797887

Reorder the terms:
-10 + x = 8.717797887

Solving
-10 + x = 8.717797887

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 8.717797887 + 10

Combine like terms: -10 + 10 = 0
0 + x = 8.717797887 + 10
x = 8.717797887 + 10

Combine like terms: 8.717797887 + 10 = 18.717797887
x = 18.717797887

Simplifying
x = 18.717797887


Subproblem 2
x + -10 = -8.717797887

Simplifying
x + -10 = -8.717797887

Reorder the terms:
-10 + x = -8.717797887

Solving
-10 + x = -8.717797887

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -8.717797887 + 10

Combine like terms: -10 + 10 = 0
0 + x = -8.717797887 + 10
x = -8.717797887 + 10

Combine like terms: -8.717797887 + 10 = 1.282202113
x = 1.282202113

Simplifying
x = 1.282202113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.717797887, 1.282202113}

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