2(x-2)(x+5)=24

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Solution for 2(x-2)(x+5)=24 equation: 


Simplifying
2(x + -2)(x + 5) = 24

Reorder the terms:
2(-2 + x)(x + 5) = 24

Reorder the terms:
2(-2 + x)(5 + x) = 24

Multiply (-2 + x) * (5 + x)
2(-2(5 + x) + x(5 + x)) = 24
2((5 * -2 + x * -2) + x(5 + x)) = 24
2((-10 + -2x) + x(5 + x)) = 24
2(-10 + -2x + (5 * x + x * x)) = 24
2(-10 + -2x + (5x + x2)) = 24

Combine like terms: -2x + 5x = 3x
2(-10 + 3x + x2) = 24
(-10 * 2 + 3x * 2 + x2 * 2) = 24
(-20 + 6x + 2x2) = 24

Solving
-20 + 6x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-20 + -24 + 6x + 2x2 = 24 + -24

Combine like terms: -20 + -24 = -44
-44 + 6x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-44 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-22 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-22 + 3x + x2 = 0

Solving
-22 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 3x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 3x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 3x + x2 = 0 + 22
3x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
3x + x2 = 22

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 22 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + 3x + x2 = 24.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + 1.5 = 4.924428901

Simplifying
x + 1.5 = 4.924428901

Reorder the terms:
1.5 + x = 4.924428901

Solving
1.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.924428901 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.924428901 + -1.5
x = 4.924428901 + -1.5

Combine like terms: 4.924428901 + -1.5 = 3.424428901
x = 3.424428901

Simplifying
x = 3.424428901


Subproblem 2
x + 1.5 = -4.924428901

Simplifying
x + 1.5 = -4.924428901

Reorder the terms:
1.5 + x = -4.924428901

Solving
1.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.924428901 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.924428901 + -1.5
x = -4.924428901 + -1.5

Combine like terms: -4.924428901 + -1.5 = -6.424428901
x = -6.424428901

Simplifying
x = -6.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.424428901, -6.424428901}
Solution
x = {3.424428901, -6.424428901}

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