Exercise 25 Page 266

Solving a radical equation usually involves three main steps.

1. Isolate the radical on one side of the equation.
2. Raise each side of the equation to a power equal to the index of the radical to eliminate the radical.
3. Solve the resulting equation. Remember to check your results!

Now we can analyze the given radical equation. sqrt(3x-8)+1=sqrt(x+5) Notice that in this equation there is an isolated radical with index equal to 2 on the right-hand side. Then, we will raise each side of the equation to the power of 2.

We obtained another radical equation. Let's now isolate the radical, sqrt(3x-8), on one side of the equation.

Now, just like before, we will raise each side of the equation to the power of 2.

We got a quadratic equation. Notice that there are many ways to solve a quadratic equation. We will use the Quadratic Formula to solve the equation. Let's determine a, b, and c. x^2-15x+44=0 ⇔ 1x^2+( - 15)x+ 44=0 We see above that a= 1, b= - 15, and c= 44. Let's substitute these values into the Quadratic Formula to solve the equation.

Now we can calculate the first root using the positive sign and the second root using the negative sign.

Checking the Solutions

Next, we will check the solutions by substituting 11 and 4 for x into the original equation. If the substitution produces a true statement, we know that our answer is correct. If it does not, then it is an extraneous solution. Let's first check the 11.

Because our substitution produced a false statement, we know that our answer, x=11, is not correct. Let's check now the 4.

Because our substitution produced a true statement, we know that our answer, x=4, is correct.