0=5x^2+80x+80

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Solution for 0=5x^2+80x+80 equation: 


Simplifying
0 = 5x2 + 80x + 80

Reorder the terms:
0 = 80 + 80x + 5x2

Solving
0 = 80 + 80x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + -80 = -80
-80 + -80x + -5x2 = 80 + 80x + 5x2 + -80 + -80x + -5x2

Reorder the terms:
-80 + -80x + -5x2 = 80 + -80 + 80x + -80x + 5x2 + -5x2

Combine like terms: 80 + -80 = 0
-80 + -80x + -5x2 = 0 + 80x + -80x + 5x2 + -5x2
-80 + -80x + -5x2 = 80x + -80x + 5x2 + -5x2

Combine like terms: 80x + -80x = 0
-80 + -80x + -5x2 = 0 + 5x2 + -5x2
-80 + -80x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-80 + -80x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-5'.
-5(16 + 16x + x2) = 0

Ignore the factor -5.

Subproblem 1
Set the factor '(16 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
16 + 16x + x2 = 0

Solving
16 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 16x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 16x + x2 = 0 + -16

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

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

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -16 + 64

Reorder the terms:
64 + 16x + x2 = -16 + 64

Combine like terms: -16 + 64 = 48
64 + 16x + x2 = 48

Factor a perfect square on the left side:
(x + 8)(x + 8) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + 8) equal to 6.92820323 and -6.92820323.


Subproblem 1
x + 8 = 6.92820323

Simplifying
x + 8 = 6.92820323

Reorder the terms:
8 + x = 6.92820323

Solving
8 + x = 6.92820323

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + x = 6.92820323 + -8
x = 6.92820323 + -8

Combine like terms: 6.92820323 + -8 = -1.07179677
x = -1.07179677

Simplifying
x = -1.07179677


Subproblem 2
x + 8 = -6.92820323

Simplifying
x + 8 = -6.92820323

Reorder the terms:
8 + x = -6.92820323

Solving
8 + x = -6.92820323

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + x = -6.92820323 + -8
x = -6.92820323 + -8

Combine like terms: -6.92820323 + -8 = -14.92820323
x = -14.92820323

Simplifying
x = -14.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.07179677, -14.92820323}
Solution
x = {-1.07179677, -14.92820323}

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