Video: Solving Simple Radical Equations

Solve √(𝑥) − 5 = −1.

01:29

Video Transcript

Solve root 𝑥 minus five equals negative one.

Okay, to solve this equation, we don’t have to worry that there’s a square root sign involved. We just solve it the same way that we would solve any equation. And we can begin by adding five to each side. So we get root 𝑥 minus five add five, which is just root 𝑥. And then we have negative one add five, which is four. Okay, so now what we need to do, because we have root 𝑥 is equal to four, is we actually need to square both sides in order to find out what 𝑥 is.

So if we square root 𝑥, we’re just gonna get 𝑥. So we’re gonna have 𝑥 is equal to four, and then four squared because we squared that side as well. So therefore, we get that 𝑥 is equal to 16. Okay, so we’ve solved the equation for 𝑥. But let’s substitute it back in, just to double check.

So if we substitute 𝑥 equals 16 back into our original expression, we’re gonna have root 16 minus five, which is equal to four minus five, which is equal to negative one. So great, negative one is what we were looking for. So therefore, we can say that the solution to root 𝑥 minus five equals negative one is: 𝑥 is equal to 16.

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