# How do you solve 4y^2 = 25?

Mar 29, 2016

The solutions are:

color(blue)(y=-5/2

color(blue)(y=5/2

#### Explanation:

$4 {y}^{2} = 25$

$4 {y}^{2} - 25 = 0$

${\left(2 y\right)}^{2} - {5}^{2} = 0$

Applying the below mentioned property to the expression:
color(blue)(a^2- b^2 = (a+b)(a-b)

(2y)^2 - 5^2 = color(blue)((2y+5)(2y-5)

Equating each of the factors to zero , we obtain the solution:

2y + 5 = 0, color(blue)(y=-5/2

2y- 5 = 0, color(blue)(y=5/2