How do you solve using the completing the square method #x^2 +8x+14=0 #?
1 Answer
Explanation:
NOte that when you square a binomial there is always a particular pattern for the answer.
As long as
In

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

The left side is the answer to the square of a binomial;
#(x color(blue)+ 4)^2 = 2# 
Find the square root of each side.
#x + 4 = +sqrt2# 
Solve for
#x# twice, once with#+sqrt2# , once with#sqrt2#
#x = +sqrt2 4 " or " x = sqrt2 4# 7
#x = 2.586 " or " 5.414#