3x(x+7)=21

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Solution for 3x(x+7)=21 equation: 


Simplifying
3x(x + 7) = 21

Reorder the terms:
3x(7 + x) = 21
(7 * 3x + x * 3x) = 21
(21x + 3x2) = 21

Solving
21x + 3x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 21x + 3x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 7x + x2) = 0

Ignore the factor 3.

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

Simplifying
-7 + 7x + x2 = 0

Solving
-7 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 7 + 12.25

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

Combine like terms: 7 + 12.25 = 19.25
12.25 + 7x + x2 = 19.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
x + 3.5 = 4.387482194

Simplifying
x + 3.5 = 4.387482194

Reorder the terms:
3.5 + x = 4.387482194

Solving
3.5 + x = 4.387482194

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 = 4.387482194 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.387482194 + -3.5
x = 4.387482194 + -3.5

Combine like terms: 4.387482194 + -3.5 = 0.887482194
x = 0.887482194

Simplifying
x = 0.887482194


Subproblem 2
x + 3.5 = -4.387482194

Simplifying
x + 3.5 = -4.387482194

Reorder the terms:
3.5 + x = -4.387482194

Solving
3.5 + x = -4.387482194

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 = -4.387482194 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.387482194 + -3.5
x = -4.387482194 + -3.5

Combine like terms: -4.387482194 + -3.5 = -7.887482194
x = -7.887482194

Simplifying
x = -7.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.887482194, -7.887482194}
Solution
x = {0.887482194, -7.887482194}

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