x(x^2+9x+7)=0

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Solution for x(x^2+9x+7)=0 equation: 


Simplifying
x(x2 + 9x + 7) = 0

Reorder the terms:
x(7 + 9x + x2) = 0
(7 * x + 9x * x + x2 * x) = 0
(7x + 9x2 + x3) = 0

Solving
7x + 9x2 + x3 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 9x + x2 = 0

Solving
7 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -7 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -7 + 20.25

Combine like terms: -7 + 20.25 = 13.25
20.25 + 9x + x2 = 13.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
x + 4.5 = 3.640054945

Simplifying
x + 4.5 = 3.640054945

Reorder the terms:
4.5 + x = 3.640054945

Solving
4.5 + x = 3.640054945

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.640054945 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.640054945 + -4.5
x = 3.640054945 + -4.5

Combine like terms: 3.640054945 + -4.5 = -0.859945055
x = -0.859945055

Simplifying
x = -0.859945055


Subproblem 2
x + 4.5 = -3.640054945

Simplifying
x + 4.5 = -3.640054945

Reorder the terms:
4.5 + x = -3.640054945

Solving
4.5 + x = -3.640054945

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.640054945 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.640054945 + -4.5
x = -3.640054945 + -4.5

Combine like terms: -3.640054945 + -4.5 = -8.140054945
x = -8.140054945

Simplifying
x = -8.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.859945055, -8.140054945}
Solution
x = {0, -0.859945055, -8.140054945}

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