-4-5(x+8)x=

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Solution for -4-5(x+8)x= equation: 


Simplifying
-4 + -5(x + 8) * x = 0

Reorder the terms:
-4 + -5(8 + x) * x = 0

Reorder the terms for easier multiplication:
-4 + -5x(8 + x) = 0
-4 + (8 * -5x + x * -5x) = 0
-4 + (-40x + -5x2) = 0

Solving
-4 + -40x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 40x + 5x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + 40x + 5x2)' equal to zero and attempt to solve:

Simplifying
4 + 40x + 5x2 = 0

Solving
4 + 40x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.8 + 8x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + 8x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + 8x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + 8x + x2 = 0 + -0.8
8x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
8x + x2 = -0.8

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -0.8 + 16

Reorder the terms:
16 + 8x + x2 = -0.8 + 16

Combine like terms: -0.8 + 16 = 15.2
16 + 8x + x2 = 15.2

Factor a perfect square on the left side:
(x + 4)(x + 4) = 15.2

Calculate the square root of the right side: 3.898717738

Break this problem into two subproblems by setting 
(x + 4) equal to 3.898717738 and -3.898717738.


Subproblem 1
x + 4 = 3.898717738

Simplifying
x + 4 = 3.898717738

Reorder the terms:
4 + x = 3.898717738

Solving
4 + x = 3.898717738

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.898717738 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.898717738 + -4
x = 3.898717738 + -4

Combine like terms: 3.898717738 + -4 = -0.101282262
x = -0.101282262

Simplifying
x = -0.101282262


Subproblem 2
x + 4 = -3.898717738

Simplifying
x + 4 = -3.898717738

Reorder the terms:
4 + x = -3.898717738

Solving
4 + x = -3.898717738

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.898717738 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.898717738 + -4
x = -3.898717738 + -4

Combine like terms: -3.898717738 + -4 = -7.898717738
x = -7.898717738

Simplifying
x = -7.898717738


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.101282262, -7.898717738}
Solution
x = {-0.101282262, -7.898717738}

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