Question Video: Solving Quadratic Equations Mathematics • 8th Grade

Solve 2(𝑥 + 4)² = 162.

02:37

Video Transcript

Solve two multiplied by all of 𝑥 plus four all squared equals one hundred and sixty two. So we can see the only thing we can get rid of away from the 𝑥 side is this two multiplied by. We know the opposite of times by is divide by, so now we must divide both sides by two. This will give us 𝑥 plus four all squared on the left-hand side and eighty one on the right. And now we have two options here. We can either take roots, which in this case we’re going to do cause that’s what the video is about. Or we could know that 𝑥 plus four all squared is the same as. And we could multiply out those brackets using foil. And then we could get a quadratic that we would be able to solve. Or if we couldn’t factor it, then maybe we would use a quadratic formula. But in this case it’s a lot quicker if we just take roots.

So doing that on the left-hand side, we get 𝑥 plus four. But the right-hand side, we end up with two options. We end up with nine or negative nine. Because we’ve just shown in the example before if we’ve got negative nine and we multiplied it by negative nine, we get positive eighty-one. And then if we have nine And multiplied it by nine, we also get positive eighty-one. So square rooting the eighty-one gives us plus or minus nine.

And now we have two options for a root. We have an option where the nine is positive and we have one for where it’s negative. So in the case where it is positive, we’ve got nine and then we take away four. And we know that nine take away four is just five. And in the case where it’s negative, we’ve got negative nine take away four. And negative nine take away four is equal to negative thirteen. So there we have it. We have solved by taking roots for this quadratic. And it’s a lot simpler than as we said multiplying out the brackets and then putting it into a quadratic and finding out if we can factor it or not. In this case, it’s a lot easier just to take roots. But the most important thing is remembering that plus or minus when we square root.

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