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### Course: Algebra (all content)>Unit 10

Lesson 18: 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.
• 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?
• 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.
• Can the answer be represented as a decimal?
• You could, but sometimes, it's just easier to answer in fractional form. :)
(1 vote)
• At sal says that the numbers are posotive rational numbers. What does this mean?
• Positive means it is not a negative number and rational means is a number that does not have a decimal that goes on forever. Sal is basically saying this question is playing by the rules as we know at this point and there is no weird stuff going on.
• In this video how did he get d=5/2 someone please explain to me thank you.
• since (x+b)^2 = x^2 + 2bx + b^2, note that the middle term is 2b. So if 2b = 5, then b = 5/2 and b^2 = 25/4. So to complete the square, you have to divide the coefficient of the x term by 2.
• why is 2d=5?
• I'm so confused bc how did he get 5/2 and that turned into 25/4?