How do you solve using the completing the square method #2x^2+3x=20#?

1 Answer
Jun 11, 2016

Answer:

#x = 2 1/2 " or " x = -4#

Explanation:

Completing the square is based on the fact that when a binomial is squared, there is a specific relationship between the coefficients of the 2nd and 3rd terms."

#(x - 5)^2 = x^2 - 10x + 25#
Note that (-10) divided by 2 and then squared gives 25.

We have #2x^2 + 3x = 20" divide by 2 first to get " x^2#

#x^2 + 3/2 x " " = 10" "# #(3/2)÷ 2 = (3/4)#

Add #(3/4)^2# to both sides
#x^2 + 3/2 x + color(red)((3/4)^2) = 10 + color(red)((3/4)^2)#
The left side can now be written as #"(binomial)"^2#

#(x + 3/4)^2 " " = 169/16#

#x + 3/4 = +-(13/4)" find the square root of both sides"#

#x = 13/4 - 3/4 " or "x = -13/4 - 3/4#

#x = 10/4 " or " x = -16/4#

#x = 2 1/2 " or "x = -4#