x(x+5)*30=3450

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Solution for x(x+5)*30=3450 equation: 


Simplifying
x(x + 5) * 30 = 3450

Reorder the terms:
x(5 + x) * 30 = 3450

Reorder the terms for easier multiplication:
30x(5 + x) = 3450
(5 * 30x + x * 30x) = 3450
(150x + 30x2) = 3450

Solving
150x + 30x2 = 3450

Solving for variable 'x'.

Reorder the terms:
-3450 + 150x + 30x2 = 3450 + -3450

Combine like terms: 3450 + -3450 = 0
-3450 + 150x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '30'.
30(-115 + 5x + x2) = 0

Ignore the factor 30.

Subproblem 1
Set the factor '(-115 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-115 + 5x + x2 = 0

Solving
-115 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '115' to each side of the equation.
-115 + 5x + 115 + x2 = 0 + 115

Reorder the terms:
-115 + 115 + 5x + x2 = 0 + 115

Combine like terms: -115 + 115 = 0
0 + 5x + x2 = 0 + 115
5x + x2 = 0 + 115

Combine like terms: 0 + 115 = 115
5x + x2 = 115

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 115 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 115 + 6.25

Combine like terms: 115 + 6.25 = 121.25
6.25 + 5x + x2 = 121.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 121.25

Calculate the square root of the right side: 11.011357773

Break this problem into two subproblems by setting 
(x + 2.5) equal to 11.011357773 and -11.011357773.


Subproblem 1
x + 2.5 = 11.011357773

Simplifying
x + 2.5 = 11.011357773

Reorder the terms:
2.5 + x = 11.011357773

Solving
2.5 + x = 11.011357773

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 11.011357773 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 11.011357773 + -2.5
x = 11.011357773 + -2.5

Combine like terms: 11.011357773 + -2.5 = 8.511357773
x = 8.511357773

Simplifying
x = 8.511357773


Subproblem 2
x + 2.5 = -11.011357773

Simplifying
x + 2.5 = -11.011357773

Reorder the terms:
2.5 + x = -11.011357773

Solving
2.5 + x = -11.011357773

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -11.011357773 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -11.011357773 + -2.5
x = -11.011357773 + -2.5

Combine like terms: -11.011357773 + -2.5 = -13.511357773
x = -13.511357773

Simplifying
x = -13.511357773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.511357773, -13.511357773}
Solution
x = {8.511357773, -13.511357773}

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