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

1 Answer
Nov 23, 2016

Answer:

#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#