-4y^2-19y-5=0

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Solution for -4y^2-19y-5=0 equation: 


Simplifying
-4y2 + -19y + -5 = 0

Reorder the terms:
-5 + -19y + -4y2 = 0

Solving
-5 + -19y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 19y + 4y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 19y + 4y2)' equal to zero and attempt to solve:

Simplifying
5 + 19y + 4y2 = 0

Solving
5 + 19y + 4y2 = 0

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

Divide each side by '4'.
1.25 + 4.75y + y2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 4.75y + -1.25 + y2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 4.75y + y2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 4.75y + y2 = 0 + -1.25
4.75y + y2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
4.75y + y2 = -1.25

The y term is 4.75y.  Take half its coefficient (2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
4.75y + 5.640625 + y2 = -1.25 + 5.640625

Reorder the terms:
5.640625 + 4.75y + y2 = -1.25 + 5.640625

Combine like terms: -1.25 + 5.640625 = 4.390625
5.640625 + 4.75y + y2 = 4.390625

Factor a perfect square on the left side:
(y + 2.375)(y + 2.375) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(y + 2.375) equal to 2.095381827 and -2.095381827.


Subproblem 1
y + 2.375 = 2.095381827

Simplifying
y + 2.375 = 2.095381827

Reorder the terms:
2.375 + y = 2.095381827

Solving
2.375 + y = 2.095381827

Solving for variable 'y'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + y = 2.095381827 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + y = 2.095381827 + -2.375
y = 2.095381827 + -2.375

Combine like terms: 2.095381827 + -2.375 = -0.279618173
y = -0.279618173

Simplifying
y = -0.279618173


Subproblem 2
y + 2.375 = -2.095381827

Simplifying
y + 2.375 = -2.095381827

Reorder the terms:
2.375 + y = -2.095381827

Solving
2.375 + y = -2.095381827

Solving for variable 'y'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + y = -2.095381827 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + y = -2.095381827 + -2.375
y = -2.095381827 + -2.375

Combine like terms: -2.095381827 + -2.375 = -4.470381827
y = -4.470381827

Simplifying
y = -4.470381827


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.279618173, -4.470381827}
Solution
y = {-0.279618173, -4.470381827}

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