Solving an Equation with Radicals - Problem 2
Solving a equation with a radical, so the steps of solving an equation with a radical will always going to be the same. You want to isolate the radical take each side to the power to get rid of the radical you are dealing with solve for our variable, and then check your answers.
So this problem what is actually going on is we have a square root and we also have the variable again. So what’s going to end up happening is we are going to have a portion of an equation which we are going to have to factor in order to solve it.
Without getting ahead of myself let’s get to that point first. So in order to solve it we first need to isolate our radical, the square root of x is equal to x minus 2. We then want to get rid of that square root so we need to square both sides. Square root squared that just goes away leaves us with the inside and we have x minus 2².
You have to remember that we need to follow this out. Common mistake is people just want to distribute that 2 in, it’s not the same thing. So we follow this out we get x² minus 4 x plus 4. Isolate everything to one side, I always like dealing with my x² term being positive so I’m going to bring the x around if 0 is equal to x² minus 5x plus 4.
We now have a term which is a quadratic we need to factor this out, x minus 4 x minus 1 leaving us with x is equal to 4 or 1. Now with any radical equation what we are going to have to do is check your answers so we are going to plug this in to make sure they actually work.
Let’s take 4 plug it in square root of 4 is 2, 2 plus 2 is 4. So that works that’s great. Try 1 square root of 1 is 1, plus 2 is 3, 3 is not equal to 1. So what happened it we actually got a extraneous solutions one that doesn’t work which is why we have to check to make sure our answers all work. When we square each side what can happen is we can actually introduce our any answer is that isn’t going to work for this problem.
But by going through the steps for solving the equation with a quadratic we are able to get at least one answer that works.