How do you solve using the completing the square method #x^2 +8x+14=0 #?

1 Answer
Jun 16, 2016

Answer:

#x = -2.586 " or " -5.414#

Explanation:

NOte that when you square a binomial there is always a particular pattern for the answer.

#(x - 3)^2 = x^2 -6x + 9 " " (ax^2 + bx + c)#
As long as #a = 1#, then there is always the same relationship between b and c.
#"(half of b)"^2 #gives #c. " "# check #(-6 ÷ 2)^2 = (-3)^2 = 9#

In #x^2 + 8x + 14 = 0# we would like the left side to be written as

#"(binomial)"^2#

  1. Move the constant to the right side.
    #x^2 + 8x " " = -14#

  2. Add the missing term to both sides #(b/2)^2#
    #x^2 color(blue)+ 8x + color(red)16 = -14 + color(red)16#

This is the part that is COMPLETING THE SQUARE.
(Add in what is missing to form a perfect square)

  1. The left side is the answer to the square of a binomial;
    #(x color(blue)+ 4)^2 = 2#

  2. Find the square root of each side.
    #x + 4 = +-sqrt2#

  3. Solve for #x# twice, once with #+sqrt2#, once with #-sqrt2#
    #x = +sqrt2 -4 " or " x = -sqrt2 -4#7
    #x = -2.586 " or " -5.414#