Simplifying
4y^{2} + 8y + -21 = 0
Reorder the terms:
-21 + 8y + 4y^{2} = 0
Solving
-21 + 8y + 4y^{2} = 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'.
-5.25 + 2y + y^{2} = 0
Move the constant term to the right:
Add '5.25' to each side of the equation.
-5.25 + 2y + 5.25 + y^{2} = 0 + 5.25
Reorder the terms:
-5.25 + 5.25 + 2y + y^{2} = 0 + 5.25
Combine like terms: -5.25 + 5.25 = 0.00
0.00 + 2y + y^{2} = 0 + 5.25
2y + y^{2} = 0 + 5.25
Combine like terms: 0 + 5.25 = 5.25
2y + y^{2} = 5.25
The y term is 2y. Take half its coefficient (1).
Square it (1) and add it to both sides.
Add '1' to each side of the equation.
2y + 1 + y^{2} = 5.25 + 1
Reorder the terms:
1 + 2y + y^{2} = 5.25 + 1
Combine like terms: 5.25 + 1 = 6.25
1 + 2y + y^{2} = 6.25
Factor a perfect square on the left side:
(y + 1)(y + 1) = 6.25
Calculate the square root of the right side: 2.5
Break this problem into two subproblems by setting
(y + 1) equal to 2.5 and -2.5.
#### Subproblem 1

y + 1 = 2.5
Simplifying
y + 1 = 2.5
Reorder the terms:
1 + y = 2.5
Solving
1 + y = 2.5
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + y = 2.5 + -1
Combine like terms: 1 + -1 = 0
0 + y = 2.5 + -1
y = 2.5 + -1
Combine like terms: 2.5 + -1 = 1.5
y = 1.5
Simplifying
y = 1.5
#### Subproblem 2

y + 1 = -2.5
Simplifying
y + 1 = -2.5
Reorder the terms:
1 + y = -2.5
Solving
1 + y = -2.5
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + y = -2.5 + -1
Combine like terms: 1 + -1 = 0
0 + y = -2.5 + -1
y = -2.5 + -1
Combine like terms: -2.5 + -1 = -3.5
y = -3.5
Simplifying
y = -3.5
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
y = {1.5, -3.5}