-5x^2-40x-79=0

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Solution for -5x^2-40x-79=0 equation: 


Simplifying
-5x2 + -40x + -79 = 0

Reorder the terms:
-79 + -40x + -5x2 = 0

Solving
-79 + -40x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(79 + 40x + 5x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(79 + 40x + 5x2)' equal to zero and attempt to solve:

Simplifying
79 + 40x + 5x2 = 0

Solving
79 + 40x + 5x2 = 0

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

Divide each side by '5'.
15.8 + 8x + x2 = 0

Move the constant term to the right:

Add '-15.8' to each side of the equation.
15.8 + 8x + -15.8 + x2 = 0 + -15.8

Reorder the terms:
15.8 + -15.8 + 8x + x2 = 0 + -15.8

Combine like terms: 15.8 + -15.8 = 0.0
0.0 + 8x + x2 = 0 + -15.8
8x + x2 = 0 + -15.8

Combine like terms: 0 + -15.8 = -15.8
8x + x2 = -15.8

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 = -15.8 + 16

Reorder the terms:
16 + 8x + x2 = -15.8 + 16

Combine like terms: -15.8 + 16 = 0.2
16 + 8x + x2 = 0.2

Factor a perfect square on the left side:
(x + 4)(x + 4) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(x + 4) equal to 0.447213596 and -0.447213596.


Subproblem 1
x + 4 = 0.447213596

Simplifying
x + 4 = 0.447213596

Reorder the terms:
4 + x = 0.447213596

Solving
4 + x = 0.447213596

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 = 0.447213596 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0.447213596 + -4
x = 0.447213596 + -4

Combine like terms: 0.447213596 + -4 = -3.552786404
x = -3.552786404

Simplifying
x = -3.552786404


Subproblem 2
x + 4 = -0.447213596

Simplifying
x + 4 = -0.447213596

Reorder the terms:
4 + x = -0.447213596

Solving
4 + x = -0.447213596

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 = -0.447213596 + -4

Combine like terms: 4 + -4 = 0
0 + x = -0.447213596 + -4
x = -0.447213596 + -4

Combine like terms: -0.447213596 + -4 = -4.447213596
x = -4.447213596

Simplifying
x = -4.447213596


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.552786404, -4.447213596}
Solution
x = {-3.552786404, -4.447213596}

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