Algebra

Solving radical equations | Exponent expressions and equations | Algebra I | Khan Academy

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We are now required to solve the following equation 3 + the square root of 5x + 6 = 12 And the strategy that we will follow to solve this kind of The equations are that we isolate the root statement on one side Then we can even square it We get rid of the root code But we have to be careful here, because when We square the root code, we will lose the useful information That we take the root root, not Positive or negative square root We just take the positive square root. So When we get the final product, we have to make sure It is an extract of the positive square root So let’s try, let’s see what I’m talking about The first thing I want to do, is that I will isolate This is on the side of the equation. And the best way to do this Is to get rid of this 3. The best way to get rid of it Of them, by subtracting 3 from the left side of the equation. And Of course if I do that on the left side, I have to do it On the right side as well I don’t always have to say that they are equal. if The left side simplifies to The square root of 5x + 6 = 12 – 3, equal to 9. Now we can We square the two sides of the equation. It can be squared 5, the square root of 5x + 6 And we can square 9 as well. And when we do this Or when we square this, we get 5x + 6 If we square the square root of 5x + 6 We get 5x + 6. With that We lose some information, because we want to get This is if we square the negative square root of 5x + 6 That is why we have to be careful in our answers And make sure it’s correct when the main equation is It is a square root. So we got 5x + 6 on the left side, and on the right side We have 81. Now this is a direct equation I want to isolate the x statements alone. I put up 6 from both sides of the equation On the left side we get 5x, and on the right side By 75. Then we can divide both sides of the equation by 5 I’m going to do that, and the equation becomes x = – let’s see– This is equal to 15, right? 5 x 10 = 50 5 x 5 = 25, the result is 75 So we get x = 15. But we want – we have to We make sure that this is correct and achieves the equation And maybe he is It will work if we take – if this square root of negative We have to make sure that the result is correct When we apply it to the positive square root So let us apply it to the equation in our hands. We get 3 + the square root of 5 x 15 So 75 + 6 All I did here was that I took 5 x 25 and replaced it By the answer, equal to 12. So we get 3 + the square root of 75 + 6 = 81 = 12. This is the square root For 81, equal to 9 positive. So 3 + 9 = 12, so we see that the result is correct We can now feel good about it

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