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*
 

How do we Divide Algebraic Radicals ?

Question: How do we Divide Algebraic Radicals ?

Dividing Algebraic radicals are similar to Greatest Common Factor(multi-variables) that was presented last week, but dividing Algebraic radicals are a little bit easier.

An example of Dividing Algebraic radicals is, the equation below:

50x6y6−−−−−−√10x4y3−−−−−−√

There are a few steps that you need to know in order to solve the following question and questions similar it:

Step 1:  divide the coefficients of 50 and 10, then divide the variables by subtracting their exponents as shown below:

5x2y3−−−−−√

5x2y3−−−−−√

x2y3−−−−−√

5x2y3−−−−−√

5x2
3−−−−−√

−−−−−√

5x2y3−−−−−√

Step 2:  Factor out the perfect squares that are in the equation. 

**Note: In some equations the entire new radical will already be a perfect square making your job easier.

x2y2−−−−√5y−−√

Step 3: Square root the perfect squares or the radical in the front. Leaving behind the un-perfect squares.

xy5y−−√

Now try it Yourself: 

162x10y10−−−−−−−−√6x−−√

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