Raise each side of the equation to a power equal to the index of the radical to eliminate the radical.
Solve the resulting equation. Remember to check your results!
Now we can analyze the given radical equation.
x-6=sqrt(3x)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 a quadratic equation. There are many ways to solve a quadratic equation. We will use the Quadratic Formula to solve this equation. Let's determine a, b, and c.
x^2-15x+36=0 ⇔ 1x^2+( -15)x+ 36=0
We see above that a= 1, b= -15, and c= 36. 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.
x=15± 9/2
x=15+9/2
x=15-9/2
x=12
x=3
Checking the Solutions
Next, we will check the solutions by substituting 12 and 3 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 12.
