How do you solve the quadratic equation by completing the square: #y^2+3y=10#?

1 Answer
Apr 22, 2018

Answer:

#y=2 or y=-5#

Explanation:

#y^2 +3y" "= 10#

You want to add in a missing term on the left so that you have a perfect square trinomial which can then be written in the form
#(y +?)^2# This process is called 'completing the square.'

The 'missing term' is found from #(b/2)^2# and has to be added to both sides of the equation.

#y^2 +3y" "color(blue)( +(3/2)^2) = 10" " color(blue)(+(3/2)^2)#

The left side can now be written as #(y+?)^2# and the right side can be simplified.

#(y +3/2)^2 = 10 +9/4" "larr# square root both sides

#(y+3/2) = +-sqrt(10 +2 1/4) = +-sqrt(12 1/4)#

#y +3/2 = +-sqrt(49/4)#

#y = 7/2-3/2" "or" "y = -7/2-3/2#

#y = 4/2=2" "or " "y= -10/2=-5#