-4x^2-40x-93=0

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Solution for -4x^2-40x-93=0 equation: 


Simplifying
-4x2 + -40x + -93 = 0

Reorder the terms:
-93 + -40x + -4x2 = 0

Solving
-93 + -40x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(93 + 40x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(93 + 40x + 4x2)' equal to zero and attempt to solve:

Simplifying
93 + 40x + 4x2 = 0

Solving
93 + 40x + 4x2 = 0

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

Divide each side by '4'.
23.25 + 10x + x2 = 0

Move the constant term to the right:

Add '-23.25' to each side of the equation.
23.25 + 10x + -23.25 + x2 = 0 + -23.25

Reorder the terms:
23.25 + -23.25 + 10x + x2 = 0 + -23.25

Combine like terms: 23.25 + -23.25 = 0.00
0.00 + 10x + x2 = 0 + -23.25
10x + x2 = 0 + -23.25

Combine like terms: 0 + -23.25 = -23.25
10x + x2 = -23.25

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -23.25 + 25

Reorder the terms:
25 + 10x + x2 = -23.25 + 25

Combine like terms: -23.25 + 25 = 1.75
25 + 10x + x2 = 1.75

Factor a perfect square on the left side:
(x + 5)(x + 5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + 5) equal to 1.322875656 and -1.322875656.


Subproblem 1
x + 5 = 1.322875656

Simplifying
x + 5 = 1.322875656

Reorder the terms:
5 + x = 1.322875656

Solving
5 + x = 1.322875656

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 1.322875656 + -5

Combine like terms: 5 + -5 = 0
0 + x = 1.322875656 + -5
x = 1.322875656 + -5

Combine like terms: 1.322875656 + -5 = -3.677124344
x = -3.677124344

Simplifying
x = -3.677124344


Subproblem 2
x + 5 = -1.322875656

Simplifying
x + 5 = -1.322875656

Reorder the terms:
5 + x = -1.322875656

Solving
5 + x = -1.322875656

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -1.322875656 + -5

Combine like terms: 5 + -5 = 0
0 + x = -1.322875656 + -5
x = -1.322875656 + -5

Combine like terms: -1.322875656 + -5 = -6.322875656
x = -6.322875656

Simplifying
x = -6.322875656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.677124344, -6.322875656}
Solution
x = {-3.677124344, -6.322875656}

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