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

##### 2 Answers

#### Explanation:

#"express as " x^2+8x=-2#

#"to "color(blue)"complete the square"# add

#(1/2"coefficient of x-term")^2" to both sides"#

#"that is add " (8/2)^2=16" to both sides"#

#rArrx^2+8xcolor(red)(+16)=-2color(red)(+16)#

#rArr(x+4)^2=14#

#color(blue)"take the square root of both sides"#

#sqrt((x+4)^2)=+-sqrt14larr" note plus or minus"#

#rArrx+4=+-sqrt14#

#"subtract 4 from both sides"#

#xcancel(+4)cancel(-4)=+-sqrt14-4#

#rArrx=-4+-sqrt14#

Move +2 to the right side of the equation.

Then halve the coefficient of x.

Then square that same coefficient.

Since

So,

When you find the number to complete the square you must add it to both sides of the equation.

So,

=

Then factorise

Therefore, the answer is: