If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Worked example: Completing the square (intro)

Sal completes x²-44x into a perfect square. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What's the difference between a binomial and trinomial? Also, is there any other vocabulary I should know? :) Thank you
• A binomial consists of 2 terms, hence the math prefix bi which means 2, as in bicycle. In contrast, a trinomial includes 3 terms, the math prefix tri means 3, as in tricycle. Hope that helps
• I don't understand, while I'm doing completing the square, that the second variable I can't half it
Ex : x2-19x= -84
• Ruth,
x²-19x= -84
Half of 19 is 19/2 so you get to work with fractions.
19/2 squared is 361/4 so you add 361/4 to both sides.
x²-19x+361/4= -84 + 361/4
(x-19/2)² = -84+361/4 Find a common denominator
(x-19/2)² = -336/4+361/4
(x-19/2)² = -336/4+361/4
(x-19/2)² = 25/4 Take the square root of both sides
x-19/2 = ±√(25/4)
x-19/2 = ±5/2 Add 19/2 to each side
x=19/2±5/2
x=24/2 and x=14/2
x=12 and x=7

x²-19x= -84
12²-19(12)= -84
144-228 = -84
-84 = -84

7²-19(7) = -84
49-133 = -84
-84 = -84
x=12 and x=7

I hope that helps make it click for you.
• i dont understand why is C= 22
• take -44 halve it, -22, then to get C -22 squared -22 * -22 = 484
• is the graph of a perfect square an upwards parabola with an axis of symmetry?
• Yes, in fact, vertex form uses perfect squares to create parabolas
``y  = a(x – h)² + k``

As long as 'a' is positive, the graph of a perfect square will be an upwards parabola symmetric along the line x=h.
• at couldn't you just put ax squared?
• No, because it has a (+) sign in between the two (ax) terms instead of a multiplication sign. Think of it this way, if you have 1x+1x you wouldn't say 1x squared. You would say 2x. There is an invisible 1 in front of the x. Hope this helps you out! :)
• Is x equals 22 minus (plus or minus the square root of negative 484) even possible?
• No, at least not with this problem. If the problem had been an equation of:
x^2-44x = 0
Completing the square would have resulted in
x^2-44x+484 = 484
(x-22)^2 = 484
Take square root: x-22 = +/- sqrt(484)
Simplify: x = 22 +/- 22
This results in: x=22+22 = 44
And in x = 0

Note: The equation would be easier to solve using factoring.
Hope this helps.
• i dont get that pattern about (x+a) squared is because my teacher showed us a different way
• Why is it so important to make the equations perfect squares?
• If I understand your question...it's important to get a perfect square on one side of the equation to be able to take the square root of both sides.
(1 vote)
• how did he get from
x^2+2(-22)x+(-22)^2
to
(x-22)^2