How do we solve radical equations quadratically?

Question: How do we solve radical equations quadratically?

Their are several steps that you need to know in order to solve a radical equation quadratically as shown below:

3x+15−−−−−−√

=

x+5

Step 1:

Is to square both sides of the equation.

(3x+15−−−−−−√)2

=

(x+5)2

Step 2:  FOIL the left side .

3x+15

=

x2+10x+25

Step 3: set the equation to zero.

3x+15 = x2+10x+25 −3x−15 = −3x−15 0 = x2+7x+10

x2+10x+25

Step4: Factor out the equation.

0 = (x+5)(x+2)

(x+5)(x+2)

Step5 : Change the signs.

x

=

{−5,−2}

Step 6: check the numbers you received as you answer by plugging them into the original equation. If the answer on both side of the equation is the same answer for each number then you have two finale solutions, if  one of the numbers work and the other does not that means that you have one solution if neither  of the numbers work then their are no solutions.

Check x=−5:
3(−5)+15−−−−−−−−−√	=	(−5)+5
0√	=	0
0	=	0
TRUE
Check x=−2:
3(−2)+15−−−−−−−−−√	=	(−2)+5
9√	=	3
3	=	3
TRUE
Final solutions:{−5,−2}

 



TRY IT YOURSELF!!!!!!

14−10x−−−−−−−√

=

x−3

* Pay attention especially to step 6*