In Exercises 1–38, solve each radical equation._____x = √6x + 7

Question

Accepted Answer

In the given radical equation. Solve for X X equals the square root of four X plus 2 21. Possible answers being 17, negative 13 and 17, 17 and negative 13 and just 13 by itself. Now to solve this, we first want to square both sides of our equal sign to get rid of the radical. Let's go ahead and square everything. We get X squared S equals to four X plus 2 21. Now let's set everything equals to zero and solve for X subtract four X in 2 21 to get X squared minus four X minus 2 21. S equals to zero. Now, we need two factors that make up 2 21 and add up to equals negative four. If we're to fact out at 2 21 2 possible factors we can get are and 13. Let's rewrite this as X squared. A one negative forces will say negative 70 X plus 13, X minus 2 can factor in X out of the first two terms giving us X multiplied by X minus 17. And we can factor out a 13 from the last two terms to also get X minus 17. We can then rewrite this as X plus 13 multiplied by X minus 17 equals zero. Now, we can solve for X X plus 13 equals zero, X minus 17 equals zero. Gives us X equals negative 13 and X equals 17. Now let's check our answers by plugging these numbers back into our equation. For our first one, we say 17 equals the square root of four multiplied by 17 plus 2 21. You get 17 equals the square root of 68 plus 2 21 or 17 equals the square root of 2 89. You take the square root, you get 17. It's equal to 17, which is true. Let's also check negative 13 equals the square root of four multiplied by negative 13 plus 21. That gives us a square root negative 52 plus 2 which gives this negative 13 equals the square root of 1 69. Simplify this, we get negative 13 equals 13, which is not necessarily correct. We then conclude we only have one answer X equals 17 which corresponds to answer a OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 1–38, solve each radical equation._____x = √6x + 7

Key Concepts

Radical Equations

Isolating the Variable

Extraneous Solutions

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