Week 6 in Pre-Calculus 11 – Solving Radical Equations Using Factoring

I chose this because it is more challenging to me, so explaining it will be more beneficial.

To solve for x, we must first get rid of the radical by squaring both sides, but first we have to isolate the radical, rewrite the equation as

Now we can square both sides, remember that 2x+3 is a binomial, meaning squaring it will give you a trinomial.

To be able to solve for x, one side of the equation needs to equal 0, so we subtract 19x and 6 from both sides

Now we can factor it normally to get

If the answer is 0, we need to make x equal something that when multiplied by the other binomial makes a 0. This much is simple since multiplying anything by 0 gives 0, so we just need to make x equal something that results in one binomial equating to 0.

In this case, there are 2 possible answers. 1 (1 times 1 minus 1 is 0), and 3/4 (4 times 3/4 minus 3 is 0).

However, the answers won’t always be correct. We have to check the answer by using the value x to see if the equation is true.

For x=1, is true.