4x(5+x)=16

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Solution for 4x(5+x)=16 equation:


Simplifying
4x(5 + x) = 16
(5 * 4x + x * 4x) = 16
(20x + 4x2) = 16

Solving
20x + 4x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 20x + 4x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 20x + 4x2 = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-4 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + 5x + x2 = 0

Solving
-4 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5x + x2 = 0 + 4
5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
5x + x2 = 4

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 = 4 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5x + x2 = 10.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + 2.5 = 3.201562119

Simplifying
x + 2.5 = 3.201562119

Reorder the terms:
2.5 + x = 3.201562119

Solving
2.5 + x = 3.201562119

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 = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.201562119 + -2.5
x = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
x = 0.701562119

Simplifying
x = 0.701562119


Subproblem 2
x + 2.5 = -3.201562119

Simplifying
x + 2.5 = -3.201562119

Reorder the terms:
2.5 + x = -3.201562119

Solving
2.5 + x = -3.201562119

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 = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.201562119 + -2.5
x = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
x = -5.701562119

Simplifying
x = -5.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.701562119, -5.701562119}
Solution
x = {0.701562119, -5.701562119}

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