4y^2+21y+25=0

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Solution for 4y^2+21y+25=0 equation: 


Simplifying
4y2 + 21y + 25 = 0

Reorder the terms:
25 + 21y + 4y2 = 0

Solving
25 + 21y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
6.25 + 5.25y + y2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + 5.25y + -6.25 + y2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + 5.25y + y2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + 5.25y + y2 = 0 + -6.25
5.25y + y2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
5.25y + y2 = -6.25

The y term is 5.25y.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25y + 6.890625 + y2 = -6.25 + 6.890625

Reorder the terms:
6.890625 + 5.25y + y2 = -6.25 + 6.890625

Combine like terms: -6.25 + 6.890625 = 0.640625
6.890625 + 5.25y + y2 = 0.640625

Factor a perfect square on the left side:
(y + 2.625)(y + 2.625) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(y + 2.625) equal to 0.80039053 and -0.80039053.


Subproblem 1
y + 2.625 = 0.80039053

Simplifying
y + 2.625 = 0.80039053

Reorder the terms:
2.625 + y = 0.80039053

Solving
2.625 + y = 0.80039053

Solving for variable 'y'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + y = 0.80039053 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + y = 0.80039053 + -2.625
y = 0.80039053 + -2.625

Combine like terms: 0.80039053 + -2.625 = -1.82460947
y = -1.82460947

Simplifying
y = -1.82460947


Subproblem 2
y + 2.625 = -0.80039053

Simplifying
y + 2.625 = -0.80039053

Reorder the terms:
2.625 + y = -0.80039053

Solving
2.625 + y = -0.80039053

Solving for variable 'y'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + y = -0.80039053 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + y = -0.80039053 + -2.625
y = -0.80039053 + -2.625

Combine like terms: -0.80039053 + -2.625 = -3.42539053
y = -3.42539053

Simplifying
y = -3.42539053


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.82460947, -3.42539053}

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