For simplicity, we will start by replacing the variable a with the variable x.
a=sqrt(7a-6) a= x ⟶ x=sqrt(7 x-6)
Since the radical is isolated, we can raise both sides of the equation to a power equal to the index of the radical. Let's try to solve our equation using this method!
We now have a quadratic equation, and we need to find its roots. To do it, let's identify the values of a, b, and c.
x^2 -7x +6 = 0 ⇔ 1x^2+( - 7)x+ 6=0
We can see that a= 1, b= - 7, and c= 6. Let's substitute these values into the Quadratic Formula.
Using the Quadratic Formula, we found that the solutions of the given equation are x= 7± 5 2.
x=7± 5/2
x_1=7+5/2
x_2=7-5/2
x_1=12/2
x_2=2/2
x_1= 6
x_2= 1
Therefore, the solutions are x_1= 6 and x_2= 1. Recall that, at the beginning of the solution, we substituted x for a. Therefore, the solutions to the original equation are a_1= 6 and a_2= 1.
Let's check them to see if we have any extraneous solutions.
