2x(x+21)=756

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Solution for 2x(x+21)=756 equation: 


Simplifying
2x(x + 21) = 756

Reorder the terms:
2x(21 + x) = 756
(21 * 2x + x * 2x) = 756
(42x + 2x2) = 756

Solving
42x + 2x2 = 756

Solving for variable 'x'.

Reorder the terms:
-756 + 42x + 2x2 = 756 + -756

Combine like terms: 756 + -756 = 0
-756 + 42x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-378 + 21x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-378 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
-378 + 21x + x2 = 0

Solving
-378 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '378' to each side of the equation.
-378 + 21x + 378 + x2 = 0 + 378

Reorder the terms:
-378 + 378 + 21x + x2 = 0 + 378

Combine like terms: -378 + 378 = 0
0 + 21x + x2 = 0 + 378
21x + x2 = 0 + 378

Combine like terms: 0 + 378 = 378
21x + x2 = 378

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 378 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 378 + 110.25

Combine like terms: 378 + 110.25 = 488.25
110.25 + 21x + x2 = 488.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 488.25

Calculate the square root of the right side: 22.096379794

Break this problem into two subproblems by setting 
(x + 10.5) equal to 22.096379794 and -22.096379794.


Subproblem 1
x + 10.5 = 22.096379794

Simplifying
x + 10.5 = 22.096379794

Reorder the terms:
10.5 + x = 22.096379794

Solving
10.5 + x = 22.096379794

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 22.096379794 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 22.096379794 + -10.5
x = 22.096379794 + -10.5

Combine like terms: 22.096379794 + -10.5 = 11.596379794
x = 11.596379794

Simplifying
x = 11.596379794


Subproblem 2
x + 10.5 = -22.096379794

Simplifying
x + 10.5 = -22.096379794

Reorder the terms:
10.5 + x = -22.096379794

Solving
10.5 + x = -22.096379794

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -22.096379794 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -22.096379794 + -10.5
x = -22.096379794 + -10.5

Combine like terms: -22.096379794 + -10.5 = -32.596379794
x = -32.596379794

Simplifying
x = -32.596379794


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.596379794, -32.596379794}
Solution
x = {11.596379794, -32.596379794}

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