(x+4)(x)(5)=380

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Solution for (x+4)(x)(5)=380 equation: 


Simplifying
(x + 4)(x)(5) = 380

Reorder the terms:
(4 + x)(x)(5) = 380

Reorder the terms for easier multiplication:
5x(4 + x) = 380
(4 * 5x + x * 5x) = 380
(20x + 5x2) = 380

Solving
20x + 5x2 = 380

Solving for variable 'x'.

Reorder the terms:
-380 + 20x + 5x2 = 380 + -380

Combine like terms: 380 + -380 = 0
-380 + 20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-76 + 4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-76 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-76 + 4x + x2 = 0

Solving
-76 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '76' to each side of the equation.
-76 + 4x + 76 + x2 = 0 + 76

Reorder the terms:
-76 + 76 + 4x + x2 = 0 + 76

Combine like terms: -76 + 76 = 0
0 + 4x + x2 = 0 + 76
4x + x2 = 0 + 76

Combine like terms: 0 + 76 = 76
4x + x2 = 76

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 76 + 4

Reorder the terms:
4 + 4x + x2 = 76 + 4

Combine like terms: 76 + 4 = 80
4 + 4x + x2 = 80

Factor a perfect square on the left side:
(x + 2)(x + 2) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + 2) equal to 8.94427191 and -8.94427191.


Subproblem 1
x + 2 = 8.94427191

Simplifying
x + 2 = 8.94427191

Reorder the terms:
2 + x = 8.94427191

Solving
2 + x = 8.94427191

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 8.94427191 + -2

Combine like terms: 2 + -2 = 0
0 + x = 8.94427191 + -2
x = 8.94427191 + -2

Combine like terms: 8.94427191 + -2 = 6.94427191
x = 6.94427191

Simplifying
x = 6.94427191


Subproblem 2
x + 2 = -8.94427191

Simplifying
x + 2 = -8.94427191

Reorder the terms:
2 + x = -8.94427191

Solving
2 + x = -8.94427191

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -8.94427191 + -2

Combine like terms: 2 + -2 = 0
0 + x = -8.94427191 + -2
x = -8.94427191 + -2

Combine like terms: -8.94427191 + -2 = -10.94427191
x = -10.94427191

Simplifying
x = -10.94427191


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.94427191, -10.94427191}
Solution
x = {6.94427191, -10.94427191}

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