3x(3+x)=63

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Solution for 3x(3+x)=63 equation: 


Simplifying
3x(3 + x) = 63
(3 * 3x + x * 3x) = 63
(9x + 3x2) = 63

Solving
9x + 3x2 = 63

Solving for variable 'x'.

Reorder the terms:
-63 + 9x + 3x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-63 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-21 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + 3x + x2 = 0

Solving
-21 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 3x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 3x + x2 = 0 + 21

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

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

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 = 21 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 21 + 2.25

Combine like terms: 21 + 2.25 = 23.25
2.25 + 3x + x2 = 23.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.82182538 and -4.82182538.


Subproblem 1
x + 1.5 = 4.82182538

Simplifying
x + 1.5 = 4.82182538

Reorder the terms:
1.5 + x = 4.82182538

Solving
1.5 + x = 4.82182538

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 = 4.82182538 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.82182538 + -1.5
x = 4.82182538 + -1.5

Combine like terms: 4.82182538 + -1.5 = 3.32182538
x = 3.32182538

Simplifying
x = 3.32182538


Subproblem 2
x + 1.5 = -4.82182538

Simplifying
x + 1.5 = -4.82182538

Reorder the terms:
1.5 + x = -4.82182538

Solving
1.5 + x = -4.82182538

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 = -4.82182538 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.82182538 + -1.5
x = -4.82182538 + -1.5

Combine like terms: -4.82182538 + -1.5 = -6.32182538
x = -6.32182538

Simplifying
x = -6.32182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.32182538, -6.32182538}
Solution
x = {3.32182538, -6.32182538}

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