In Exercises 1–38, solve each radical equation._____√2x + 1 = x -...

Question

In Exercises 1–38, solve each radical equation._____√2x + 1 = x - 7

Accepted Answer

In the given radical equation solve for X where we have the square root of four X minus 19 equals X minus 10. Possible answers being 7, 17, negative seven and 17 7 by itself and 17th by itself to solve this, we can first try and eliminate the radical to do that. We will take both sides and square, both of them on the left side or X minus 19. What he calls the right side as X minus 10 squared, X minus 10 squared expands to X squared minus 20 X plus 100 to solve this, we will move everything to one side and set it equals to zero to track for X and add 19. We then get zero equals X squared minus 24 X plus 1 19. No factor are quadratic. We know this here. Our factors of 1 19 will be 11 19 and seven and 17. We know this 1 19 is positive. So we can rewrite our negative minus seven, X minus 17, X plus 1 19. Then factor in X the first two giving us X minus seven in factor a 17 from the other one and 17, X minus seven. Like so we then get the factors X minus seven and X minus 17. Save them equal to zero. We get X minus seven equals zero, X minus 17 equals zero. And as a result, X equals seven and X equals 17. Now we can check to see if these are both solutions to do that. We'll plug our new values back into the original equation. Let's say we take seven first, we will get the square root or multiplied by seven minus 19 and that should equal seven minus 10. We get the square root 28 minus 19 equals negative three 28 minus 19 is nine. So we get three equals negative three. That is not true. Let's also check X equals 17, X equals 17. We get the square root four multiplied by 17 minus equals 17 minus square root of 68 minus 19 equals seven, 68 minus 19 is 49 which we know that is seven, seven is equal to seven. So we can confirm our solution is X equals 17. This corresponds to answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 1–38, solve each radical equation._____√2x + 1 = x - 7

Key Concepts

Radical Equations

Isolating the Variable

Extraneous Solutions

Watch next