-2x(x-10)=24

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Solution for -2x(x-10)=24 equation: 


Simplifying
-2x(x + -10) = 24

Reorder the terms:
-2x(-10 + x) = 24
(-10 * -2x + x * -2x) = 24
(20x + -2x2) = 24

Solving
20x + -2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 20x + -2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 10x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 10x + -1x2)' equal to zero and attempt to solve:

Simplifying
-12 + 10x + -1x2 = 0

Solving
-12 + 10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
12 + -10x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -10x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -10x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -10x + x2 = 0 + -12
-10x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-10x + x2 = -12

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -12 + 25

Reorder the terms:
25 + -10x + x2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + -10x + x2 = 13

Factor a perfect square on the left side:
(x + -5)(x + -5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -5) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + -5 = 3.605551275

Simplifying
x + -5 = 3.605551275

Reorder the terms:
-5 + x = 3.605551275

Solving
-5 + x = 3.605551275

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 3.605551275 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.605551275 + 5
x = 3.605551275 + 5

Combine like terms: 3.605551275 + 5 = 8.605551275
x = 8.605551275

Simplifying
x = 8.605551275


Subproblem 2
x + -5 = -3.605551275

Simplifying
x + -5 = -3.605551275

Reorder the terms:
-5 + x = -3.605551275

Solving
-5 + x = -3.605551275

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -3.605551275 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.605551275 + 5
x = -3.605551275 + 5

Combine like terms: -3.605551275 + 5 = 1.394448725
x = 1.394448725

Simplifying
x = 1.394448725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.605551275, 1.394448725}
Solution
x = {8.605551275, 1.394448725}

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