Question

How do you solve using the completing the square method `y^2+4y-45=0`?

Answer 1

`y=-9 or y=5`

Explanation:

To complete the square we use `1/2` of the `y` coefficient as follows:

`y^2 + 4y -45 = 0`
`:. (y^2 + 1/2(4))^2 - (1/2(4))^2 - 45 = 0`
`:. (y^2 + 2)^2 - (2)^2 - 45 = 0`
`:. (y^2 + 2)^2 - 4 - 45 = 0`
`:. (y^2 + 2)^2 - 49 = 0`
`:. (y^2 + 2)^2 = 49`

We can now take the square root remembering that when we do so we get two solutions as `a^2 = b <=> a = +- sqrtb`

`:. y^2 + 2 = +-7`
`:. y^2 = -2+-7`

Yielding the two solutions:

`y=-9 or y=5`