Solve each equation. √2x=√(3x+12)-2

Question

Accepted Answer

Hello, everyone in this video, we're going to be looking at this practice problem where we want to solve for X in the equation, the square root of three X is equal to the square root of four x plus 16 -2. So in this case, you can see that we have X on both sides of the equation, the left hand side and the right hand side. So in order to solve for X, I want to move all of the excess to one side and try to isolate them, but they're stuck in a square root. So I need to square both sides. Well, this right hand side is a bit heavy. So before I square both sides, I'm actually going to move this to over to the left hand side to make it easier to square. So if I do that, I now have the square root of three X plus two is equal to the square root at four X plus 16. And now when I square both sides, the left hand side becomes the square root of three X plus two times the square root of three X plus two because of that squared and my right hand side, the square root gets erased or eliminated by the exponents. So I'm left with just four X plus 16. I can do the multiplication on the left hand side. So the square root of three X and the times the square root of three X is simply three X without the square root. Then I have the square root of three X times two is two times the square root of three X and I have that same multiplication again, two times the square root of three X. And then I have two times two, which is four, I can combine these middle terms to give me four times the square root of three x. And that's still equal to four x plus 16. From here, I'm gonna wanna move these terms over to the right. So also Chock three X -4 from both sides. So those get eliminated and I'm left with four times the square root of 3X and that's equal to four X -3, X is X and 16 -4 is 12. And again, we see X is stuck in a square root. So I'm gonna square both sides once again. So that leaves me with four squared times three X. Well, four squared is four times four, which is 16, that's equal to X plus 12 times X plus 12. And I'll go ahead and expand this once again. And I'm actually going to write, continue simplifying it over here. So I have 16 times three is equal to 48 x. That's equal to X times X is X squared, X times 12 is 12, X, 12 times X is 12 X and 12 times 12 is 1 44. And once again, I can combine these middle terms. So 12 X plus 12, X is 20 for X, but I still have this 48 X on the left hand side. So I'm going to subtract it from both sides. So that leaves me with zero is equal to X squared and positive 24 X minus 48 X is negative 24 X plus 144. And here you can see that we have a quadratic equation. So we want to find two terms whose first term multiplied two X squared well, X times X is X squared. And we want the second terms to Multiply 2, 1 44. So we can do 12 Because 12 times 12 is 1 44. And if I test this, these factory ization, I have X times X is X squared, X times 12 is positive 12 X and 12 times X is positive 12 X again. And then we have 12 times 12 which is 144. If I combine the middle terms, I have X squared plus 24 X plus 1 44 will notice the middle term is positive and we actually wanted it to be negative. So that means I can change the value Here. So X -12 times X -12. And now the sign for these mental terms will be negative giving me X squared minus 24 X plus 144. So now I get back the original equation from my factory ization And we can see that X -12 is our factory ization. Well, X -12 Squared. So that means that when I solve for X using this factory ization, I have X minus 12 squared is equal to zero. I take the square root of both sides. I have X minus 12 is equal to the square root of zero, which is still zero. I'll add 12 and I get X is equal to 12. So this becomes my solution for X in this equation. And you can see that answer choice a list 12. So hopefully this video helped and see you next time.

Solve each equation. √2x=√(3x+12)-2

Key Concepts

Square Root Equations

Isolating Variables

Checking for Extraneous Solutions

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