Solve each equation using the square root property. See Example 2...

Question

Solve each equation using the square root property. See Example 2. (4x + 1)^2 = 20

Accepted Answer

Hello, everyone. We're gonna use the square root rule to solve the equation. Seven X plus one squared equals 96. So the square root rule says that I can use a square root, cancel out a square. So in this case, I'm gonna take the square root of both sides because what I do to one side, I need to do the other. So I can get that square off of the quantity seven X plus one. So when I do this, it cancels out and I have seven X plus one on my left hand side equals the square to 96. So 96 does not look like it's a perfect square thinking about what can I break that down into? And I think I can break it down into the square to 16 times the square to six. So seven X plus one is staying the same for now, the square to 16 is plus or minus four and radical six can't be simplified. So right now I have seven X plus one equals plus or minus four radical six. At this point, I need to break this into two equations because I haven't found what X equals yet. But I have a positive and a negative option on the right hand side. So rewriting them going to the left, I'm gonna do seven X plus one equals four radical six and going to the right, I'm gonna do seven X plus one equals negative four radical six. I'm gonna solve them each independently and then we'll have our two answers. So for seven X plus one equals four radical six, I'm gonna start by subtracting one from both sides. So I have seven X equals negative one plus four radical six. Then dividing both sides by seven. Here I get that X would equal negative one plus four radical 6/7. So there's one of our solutions, we need to do the next side. So now I have seven X plus one equals negative four radical six. So same process, I'm gonna subtract one from both sides. So I have seven X equals negative one minus four radical six. And then dividing both sides by seven, I get that X equals negative one minus four radical six over seven. So there's my other value comparing it to my answer choices. It appears to be answer choice. C have a nice day.

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Solve each equation using the square root property. See Example 2. (4x + 1)^2 = 20

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