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## Algebra 1

### Course: Algebra 1>Unit 14

Lesson 9: Strategizing to solve quadratic equations

# Strategy in solving quadratic equations

Based on the initial form of a quadratic equation, we can determine which solution methods are and aren't appropriate. Created by Sal Khan.

## Want to join the conversation?

• Completing The Square seems much faster and easier then plugging numbers into the Quadratic Equation.
When should we use the Quadratic Equation over Completing The Square? or are both valid and it's just personal preference?
• I would argue against what RN said and say completing the square is more useful, perhaps not easier though. completing the square gets you vertex form, which would allow you to more clearly graph the function.
• At ,(or really at ) can't we just say that (x+3) = -1? Sal says that it wouldn't work to say that (x+3) = 0 because the equation is (x+3)(x+1) = -1, and just jumping to x = -3 wouldn't work because that only works for x+3 = 0. But couldn't we just say that x = -4, because x+3=-1 = -4+3=-1?

So we just say that x = -4 or x = -2 instead of x = -3 or x = -1?

Does this make sense?
• It won't work because if x=-4, then it will be (4+3)(4+1)=-1, and 7*5 is not -1. The easiest way is to use the 0 property when factoring, because 0 times anything is 0. If not, there's going to me lots of guessing and error.

Hope this helps!
(1 vote)
• It seems like completing the square takes up much less time. At what points do we use completing the square or do we use the quadratic formula
• At about in the video for the third strategy in solving a quadratic equation, why doesn't Sal add -1 to both sides, instead of right off the bat, factoring the left hand side?
LATER: Actually, nevermind. He goes on to say that the third example needs to be equal to 0 in order to get the solutions.

What is the zero product property? (Sal mentions this at the last few seconds of the video.)
• If you multiply two (or more) things and the product is 0, then one or the other or both have to equal zero. That is why if we have (x+3)(x+1)=0, we have to say either x+3=0 or x+1=0.
• Is there a specific way to tell which method to use? or is it a guess and check?
• At about , why can't you take x^2=-4x -4, and take the square root for

x=+-2x+-2

And then add or subtract the 2x from the right side to make either

3x=+-2 (and divide both sides by 3)
or
-1x=+-2
?

Thanks!
(1 vote)
• because the √(4x-4) cannot be simplified except to take out a 4 to get 2√(x-1). All you did was divide it by 2, not take the square root
• so for x^2+5x-3=-2+5x I first cancel the 5s, and then I work my way to the answer being x=±√1. Is that correct?
(1 vote)
• Yes, and the square root of 1 is just 1, so you can simply say x = 1 or -1. Hope this helps.