9x(x+7)=81

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Solution for 9x(x+7)=81 equation: 


Simplifying
9x(x + 7) = 81

Reorder the terms:
9x(7 + x) = 81
(7 * 9x + x * 9x) = 81
(63x + 9x2) = 81

Solving
63x + 9x2 = 81

Solving for variable 'x'.

Reorder the terms:
-81 + 63x + 9x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + 63x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-9 + 7x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-9 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 7x + x2 = 0

Solving
-9 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 7x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 7x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 7x + x2 = 0 + 9
7x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
7x + x2 = 9

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 = 9 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 9 + 12.25

Combine like terms: 9 + 12.25 = 21.25
12.25 + 7x + x2 = 21.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
x + 3.5 = 4.609772229

Simplifying
x + 3.5 = 4.609772229

Reorder the terms:
3.5 + x = 4.609772229

Solving
3.5 + x = 4.609772229

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 = 4.609772229 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.609772229 + -3.5
x = 4.609772229 + -3.5

Combine like terms: 4.609772229 + -3.5 = 1.109772229
x = 1.109772229

Simplifying
x = 1.109772229


Subproblem 2
x + 3.5 = -4.609772229

Simplifying
x + 3.5 = -4.609772229

Reorder the terms:
3.5 + x = -4.609772229

Solving
3.5 + x = -4.609772229

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 = -4.609772229 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.609772229 + -3.5
x = -4.609772229 + -3.5

Combine like terms: -4.609772229 + -3.5 = -8.109772229
x = -8.109772229

Simplifying
x = -8.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.109772229, -8.109772229}
Solution
x = {1.109772229, -8.109772229}

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