Solve each equation. √(x+3)-1=4

Name: Problem 55, Chapter 9: Algebra 2
Uploaded: 2020-04-14T14:31:32-08:00
Duration: 3 min 36 s
Channel: Connor Wagner
Description: Solve each equation. √(x+3)-1=4

Key Concepts

Radical Equations

Radical equations are equations in which the unknown variable appears under a radical sign, such as a square root. Solving these equations typically involves isolating the radical expression on one side of the equation so that further algebraic operations can eliminate the radical, making the equation easier to solve.

Isolating the Radical

This concept involves rearranging the equation to have the radical on one side and all other terms on the opposite side. This step is crucial because it prepares the equation for the application of operations—typically raising both sides to a suitable power—that remove the radical and simplify the equation.

Squaring Both Sides

Squaring both sides is a common technique used to eliminate a square root from an equation. After isolating the radical, both sides are squared to produce an equation without the square root, which can then be solved using standard algebraic methods. However, this step may introduce extraneous solutions, which must be checked.

Extraneous Solutions

Extraneous solutions are potential solutions that emerge from the process of manipulating equations, especially when both sides are squared. These solutions may not satisfy the original equation, so it is important to substitute them back into the original equation to verify their validity.

Transcript

00:01 All right, so what's the problem we have here? the problem we're trying to solve is what is the square root of x plus 3 minus 1 equals 4.

00:13 This whole thing is under the radical here.

00:16 And so what we want to think about when we're solving equation is what all of this means.

00:22 And what this is saying, an equal sign is telling us is that everything on the left is equivalent to everything on the right.

00:28 So i like to think of this as a balance and think of it as weight.

00:31 So everything over here weighs the same amount as everything over on this side.

00:37 And so what we're going to do is we're going to try and find out what this unknown, you can think of it as a weight is.

00:43 And if you stepped on a scale and you had a box in your hand and clothes on, would you know what you weighed? no, you wouldn't because you have all that stuff on the scale with you.

00:52 So what you're going to have to do is we have to get rid of all this.

00:54 We have to find a way to get rid of the three and the square root symbol in the minus 1.

01:02 And so if we can get rid of all that, we'll just have the x and we'll know what it equals.

01:06 So how do we do that? what we're going to do is we're going to use inverse operations and work backwards through the order of operations.

01:12 So we're going to get rid of this minus 1 first.

01:16 And so how are we going to get rid of a minus 1? well, the inverse of minus 1 is going to be adding one.

01:21 And think about this scale.

01:22 If i add 1 pound to this side of the scale, to keep everything balanced, i'm going to have to add one over here.

01:29 And a minus one and a plus one is going to cancel out to zero.

01:35 So we got rid of that and that's what we wanted...

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