4x(x+30)=360

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Solution for 4x(x+30)=360 equation: 


Simplifying
4x(x + 30) = 360

Reorder the terms:
4x(30 + x) = 360
(30 * 4x + x * 4x) = 360
(120x + 4x2) = 360

Solving
120x + 4x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 120x + 4x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-90 + 30x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-90 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 30x + x2 = 0

Solving
-90 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 30x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 30x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 30x + x2 = 0 + 90
30x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
30x + x2 = 90

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 90 + 225

Reorder the terms:
225 + 30x + x2 = 90 + 225

Combine like terms: 90 + 225 = 315
225 + 30x + x2 = 315

Factor a perfect square on the left side:
(x + 15)(x + 15) = 315

Calculate the square root of the right side: 17.748239349

Break this problem into two subproblems by setting 
(x + 15) equal to 17.748239349 and -17.748239349.


Subproblem 1
x + 15 = 17.748239349

Simplifying
x + 15 = 17.748239349

Reorder the terms:
15 + x = 17.748239349

Solving
15 + x = 17.748239349

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 17.748239349 + -15

Combine like terms: 15 + -15 = 0
0 + x = 17.748239349 + -15
x = 17.748239349 + -15

Combine like terms: 17.748239349 + -15 = 2.748239349
x = 2.748239349

Simplifying
x = 2.748239349


Subproblem 2
x + 15 = -17.748239349

Simplifying
x + 15 = -17.748239349

Reorder the terms:
15 + x = -17.748239349

Solving
15 + x = -17.748239349

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -17.748239349 + -15

Combine like terms: 15 + -15 = 0
0 + x = -17.748239349 + -15
x = -17.748239349 + -15

Combine like terms: -17.748239349 + -15 = -32.748239349
x = -32.748239349

Simplifying
x = -32.748239349


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.748239349, -32.748239349}
Solution
x = {2.748239349, -32.748239349}

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