Completing the square process, I don't quite understand it yet, can someone explain step by step? X^2+10x+16=0

1 Answer
Somebody N.
Jun 17, 2018

#color(blue)(x=-8 " and " x=-2)#

Explanation:

#x^2+10x+16=0#

Step 1.

Divide right through by the coefficient of #x^2# if this is not 1.

We have a coefficient of 1, so we don't need to do this.

Step 2.

Move the constant to the #RHS#

#x^2+10x=-16#

Step 3.

Add to both sides the square of half the coefficient of #x#.

In this example this is #(5)^2# do not expand this, i.e. don't add it as 25.

#x^2+10x+(5)^2=-16+(5)^2#

Step 4.

Form a binomial on the #LHS#

Take away the #10x# to get:

#x^2+(5)^2#

Then we have:

#(x+5)^2#

And all together:

#(x+5)^2=-16+(5)^2#

Step 5.

Simplify #RHS#

#(x+5)^2=-16+25#

#(x+5)^2=9#

Step 6.

Take the square root of both sides:

#sqrt((x+5)^2)=sqrt(9)#

#x+5=+-3#

i.e.

#x+5=+3#

#x+5=-3#

Step 7.

Subtract five from both sides:

#x=-3-5=-8#

#x=3-5=-2#

So the solutions are:

#x=-8 and x=-2#

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