2x(x+7)=24

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Solution for 2x(x+7)=24 equation: 


Simplifying
2x(x + 7) = 24

Reorder the terms:
2x(7 + x) = 24
(7 * 2x + x * 2x) = 24
(14x + 2x2) = 24

Solving
14x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 14x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + 7x + x2 = 0

Solving
-12 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 7x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 7x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 7x + x2 = 0 + 12
7x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
7x + x2 = 12

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 12 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + 7x + x2 = 24.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + 3.5 = 4.924428901

Simplifying
x + 3.5 = 4.924428901

Reorder the terms:
3.5 + x = 4.924428901

Solving
3.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.924428901 + -3.5
x = 4.924428901 + -3.5

Combine like terms: 4.924428901 + -3.5 = 1.424428901
x = 1.424428901

Simplifying
x = 1.424428901


Subproblem 2
x + 3.5 = -4.924428901

Simplifying
x + 3.5 = -4.924428901

Reorder the terms:
3.5 + x = -4.924428901

Solving
3.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.924428901 + -3.5
x = -4.924428901 + -3.5

Combine like terms: -4.924428901 + -3.5 = -8.424428901
x = -8.424428901

Simplifying
x = -8.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.424428901, -8.424428901}
Solution
x = {1.424428901, -8.424428901}

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