How do you solve using the completing the square method x2+8x+14=0?

1 Answer
EZ as pi
Jun 16, 2016

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=x2−6x+9 (ax2+bx+c)
As long as a=1, then there is always the same relationship between b and c.
(half of b)2gives c. check (−6÷2)2=(−3)2=9

In x2+8x+14=0 we would like the left side to be written as

(binomial)2

  1. Move the constant to the right side.
    x2+8x =−14

  2. Add the missing term to both sides (b2)2
    x2+8x+16=−14+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+4)2=2

  2. Find the square root of each side.
    x+4=±√2

  3. Solve for x twice, once with +√2, once with −√2
    x=+√2−4 or x=−√2−47
    x=−2.586 or −5.414

Related questions
See all questions in Completing the Square
Impact of this question
5092 views around the world
You can reuse this answer
Creative Commons License