www.greenemath.... / mathematicsbyjgreene In this lesson, we review the square root property. This allows us to solve quadratic equations of the form: x^2 = k , (ax + b)^2 = k
100th attempt at college algebra, I feel like it's the only class standing in the way of my degree. You speak so clearly and I can't thank you enough for uploading videos. I could cry because I can now see a tiny light at the end of this forever tunnel. Thank you.
We're doing online class and the teacher can't teach properly because of weak Internet the math is so much harder right now. This is our subject a while ago and I didn't understand anything so thank you much 💗 I can do my homework now. God Bless you.
I wanted to double check my understanding that when we take the root of any single term we end up with both a positive and negative result. However, when we take the root of an expression such as (x-7)^2 we only end up with the expression, without the need for two solutions. My apologies if that is a silly concept, would you mind clarifying if that is incorrect?
There is some nuisance to this that is often not explained. sqrt[(x - 7)^2] = |x - 7| What ends up happening is that the above is baked into a rule known as the square root property. if x^2 = k , then x = ± k Where does that come from? sqrt(x^2) = sqrt(k) |x| = sqrt(k) x = sqrt(k) or x = -sqrt(k) This can be extended to your situation: (x - 7)^2 = 64 By the square root property: x - 7 = ±sqrt(64) Where does that come from? sqrt[(x - 7)^2] = sqrt(64) |x - 7| = sqrt(64) x - 7 = sqrt(64) or x - 7 = -sqrt(64)
Essentially, flipping signs on both the constant on the right side of the equation and the expression on the left side of the equation would be redundant at best. It is clearer, more simple, and easier to avoid silly mistakes if you only flip signs on the constant than flipping signs on the expression.
@HastiinTliziYazhi It would appear that you are lost, so maybe I can help. Let's start with something kind of basic and work our way up to the square root property. When we square a number, we lose information about the sign. (-2)^2 = 4 2^2 = 4 So when I have an equation such as: x^2 = 4 x = 2 or x = -2 This is the basis for the square root property. x^2 = k x = ± sqrt(k) A simple example. x^2 = 9 Using the square root property: x = ± sqrt(9) = ± 3 This is because x could be -3 or x could be +3, since squaring a number results in a loss of information about the sign. Okay, now for the other cases: (x - a)^2 = k Here it's the same thing, you are squaring a quantity now (x - a), so you are again losing information about the sign. x - a = ± sqrt(k) x = ± sqrt(k) + a Let's go back to the example: (x - 7)^2 = 64 x - 7 = sqrt(64) or x - 7 = -sqrt(64) x - 7 = 8 or x - 7 = -8 x = 15 or x = -1 Let's plug in now, I think this might make it makes sense: (15 - 7)^2 = 64 8^2 = 64 (-1 - 7)^2 = 64 (-8)^2 = 64 See how we ended up saying that 64 could come from -8 or +8?
yes God bless you , you are a very clear and understanding teacher, the multiple problems is very helpful and the breakdown in many ways is better to remember
What a Amazing Tutorial, better than my math teacher LoL my math teacher she teach a little bit faster, but you, you explain one by one, thank thank you so much for this vid, SORRY IF MY ENGLISH ARE NOT GOOD HEHEHE
16x^2 - 56x + 49 is a perfect square trinomial, which means it can be factored into a binomial squared: 16x^2 - 56x + 49 = (4x - 7)^2 If you were to FOIL out (4x - 7)(4x - 7), you would get back to the 16x^2 - 56x + 49 at the beginning of the problem.
@@Greenemath thank you, I get it now, the minus 56 is got from adding the two negative 7. Goodness do I feel stupid, but I’m glad I asked, it was driving me crazy😊
