Choose and apply the best method to solve the given quadratic equation. 4x2+16x+12=04x^2+16x+12=0

x=−3,x=−1x=-3,x=-1x=−3,x=−1

Choose and apply the best method to solve the given quadratic equation. 4 x 2 + 16 x + 12 = 0 4x^2+16x+12=0

Hey, everyone. In this problem, I wanna choose and apply the best method to solve this quadratic equation, 4x squared plus 16x plus 12 equals 0. Now, looking at this equation something that immediately sticks out to me is I can factor out a greatest common factor. So let's go ahead and do that before going any further. So my greatest common factor here between all of these is 4. So if I go ahead and divide this whole quadratic equation by 4, I will end up with x squared plus 4x plus 3 is equal to 0. So let's take another look at this and decide what method to continue with. Well, x squared plus 4x plus 3 equals 0 actually does have obvious factors to me here so let's go ahead and try to factor this. So our equation is already in standard form so that first step is already done. Now step 2 is to factor this completely. Now since my leading coefficient is 1 and there's not a factoring formula that I can use, I'm going to use the a c method to factor here and I want to find numbers that multiply to 3 and add to 4. Now, the numbers that I immediately think of are 1 and 3 and if I multiply 1 times 3 that gives me 3, and then if I add 1 plus 3 that gives me 4. So it looks like those are going to be my factors. So this factors into x+1x+3 and that's equal to 0. So we have factored this and now we want to set our factors equal to 0. So x equals or x plus 1 equals 0 and x plus 3 equals 0. Now let's go ahead and solve. So if I subtract 1 from both sides here I'm left with x is equal to negative 1. And then if I subtract 3 from both sides here I'm going to end up with x equals negative 3. Now I'm pretty sure that these are my solutions, but remember that you can always plug them back in to check, especially if they're really easy whole numbers like this to plug back into your original equation. So let's go ahead and plug a negative one back into our original to double check. So this is 4 times negative one squared plus 16 times negative one plus 12 equals 0. Okay. So negative one squared is just positive one, so this just becomes 4. And then 16 times negative one is gonna give me negative 16, and then plus 12 equals 0. Now 4 minuteus 16 is going to give me negative 12 and that's plus 12 equals 0. Negative 12 +12 is indeed 0, and that's equal to 0. This is definitely a true statement, so I know that I factored this correctly, and my answers are indeed x equals negative one and x equals negative 3. Remember that if the method that you chose initially doesn't work out, you can always go back to the drawing board and try a new one. It's possible that multiple methods may work for 1 or you might have chosen the wrong one and need to pick a different one. I'll see you in the next video.

Algebra & Trigonometry 때문에 힘들어하고 계신가요?

Choose and apply the best method to solve the given quadratic equation. 4x2+16x+12=04x^2+16x+12=0

다음 시청

Choose and apply the best method to solve the given quadratic equation.
$4 x^{2} + 16 x + 12 = 0$