4x(x+8)=-20-2x

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Solution for 4x(x+8)=-20-2x equation:


Simplifying
4x(x + 8) = -20 + -2x

Reorder the terms:
4x(8 + x) = -20 + -2x
(8 * 4x + x * 4x) = -20 + -2x
(32x + 4x2) = -20 + -2x

Solving
32x + 4x2 = -20 + -2x

Solving for variable 'x'.

Reorder the terms:
20 + 32x + 2x + 4x2 = -20 + -2x + 20 + 2x

Combine like terms: 32x + 2x = 34x
20 + 34x + 4x2 = -20 + -2x + 20 + 2x

Reorder the terms:
20 + 34x + 4x2 = -20 + 20 + -2x + 2x

Combine like terms: -20 + 20 = 0
20 + 34x + 4x2 = 0 + -2x + 2x
20 + 34x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
20 + 34x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 17x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 17x + 2x2)' equal to zero and attempt to solve:

Simplifying
10 + 17x + 2x2 = 0

Solving
10 + 17x + 2x2 = 0

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

Divide each side by '2'.
5 + 8.5x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8.5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 8.5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8.5x + x2 = 0 + -5
8.5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
8.5x + x2 = -5

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = -5 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = -5 + 18.0625

Combine like terms: -5 + 18.0625 = 13.0625
18.0625 + 8.5x + x2 = 13.0625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(x + 4.25) equal to 3.614208074 and -3.614208074.


Subproblem 1
x + 4.25 = 3.614208074

Simplifying
x + 4.25 = 3.614208074

Reorder the terms:
4.25 + x = 3.614208074

Solving
4.25 + x = 3.614208074

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 3.614208074 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 3.614208074 + -4.25
x = 3.614208074 + -4.25

Combine like terms: 3.614208074 + -4.25 = -0.635791926
x = -0.635791926

Simplifying
x = -0.635791926


Subproblem 2
x + 4.25 = -3.614208074

Simplifying
x + 4.25 = -3.614208074

Reorder the terms:
4.25 + x = -3.614208074

Solving
4.25 + x = -3.614208074

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -3.614208074 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -3.614208074 + -4.25
x = -3.614208074 + -4.25

Combine like terms: -3.614208074 + -4.25 = -7.864208074
x = -7.864208074

Simplifying
x = -7.864208074


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.635791926, -7.864208074}
Solution
x = {-0.635791926, -7.864208074}

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