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### Course: Algebra basics>Unit 7

Lesson 8: Factoring quadratics: Perfect squares

# Factoring perfect squares: missing values

Sal analyzes the factorization of x^2+5x+c as (x+d)^2 to find the values of the missing coefficients c and d.

## Want to join the conversation?

• At , can someone explain how d is turned into 5/2? Also explain how 2d equals 5, and not 2dx.
• Hopefully, you can see that the 2 middle terms must equal. You can use: "2dx = 5x" or you can just use Sal's version: "2d = 5". If you solve either of these for "d", you will get "d = 5/2".
-- if you start with: "2dx = 5x", you need to divide by "2x" to solve for "d"
2dx / (2x) = 5x / (2x)
d = 5x / (2x) Reduce
d = 5/2
-- if you start with "2d = 5", just divide both sides by 2 and you get d = 5/2

Hope this helps.
• So perfect square pattern is just a shortcut method like cross multiply?

And the general form if using grouping method?
• Yes... if you have a perfect square trinomial, you can use the pattern as a quicker way to do the factoring. The pattern can also be used to square 2 binomials because it creates the perfect square trinomial.
• This problem is so confusing. I can't comprehend how 5/2 would give us the answer. Aren’t the factors of d^2 suppose to equal 5x when added together?
• I'm so confused bc how did he get 5/2 and that turned into 25/4?
• Is this method used to solve linear equations?
(1 vote)
• No, linear equations are 1st degree (highest exponent = 1). Factoring is used for 2nd degree and higher equations.
• It's not a perfect square if it's a decimal or fraction though?
• Yes, decimals and fractions can be squares. For example, 0.25 is the square of 0.5, as 0.5x0.5=0.25.

Hope that helped!
• Where did you get 5/2?
(1 vote)
• When you square a binomial, you get a very specific pattern. Sal shows this using (x+d)^2 = x^2+2dx+d^2
Notice, the middle term has a coefficient of 2d, and the last term is d^2.

Sal was given x^2+5x+c and asked to find c. Using the pattern, he know that 5 = 2d. Solve it and you get d=5/2. Then again using the pattern, he knows c = d^2. So c = (5/2)^2 = 25/4.

Hope this helps.
• Why couldn't we just assume that c is the square of the middle coefficient and therefore 25, and then factor it out into (x+5)(x+5), so then d=5?
(1 vote)
• That would give you x^2+10x+25 since you end up with two 5x terms, so you have changed the problem.