About this video
Meredith solved 2(x + 4)^2 = 242 and got only x = 7, but the teacher's answers were x = 7 and x = -15. Sal checks her steps: dividing both sides by 2 was correct, but in step two she took only the positive square root of 121, missing x + 4 = -11, which gives x = -15.
You'll be able to
- find the error in a worked solution of a quadratic equation.
- explain why taking a square root needs both the positive and negative root.
- find the missing solution once the error is fixed.
Key words
- Square root
- A number that multiplies by itself to give another; 11 and -11 are both square roots of 121.
- Plus or minus (±)
- A symbol meaning both the positive and the negative value.
- Equality
- Both sides being equal; you must do the same thing to both sides to keep it.
Transcript
Meredith is solving the following problem for homework, 2 times the quantity x plus 4 squared is equal to 242. She completes the problem as seen in the steps below, and they give us the steps right over here. When she gets to school the next day, her teacher tells her that the answer's x equals 7 and x equals negative 15.
She only got x equals 7 here. In what step did she make an error? So this first step right here-- and I encourage you to pause this video and try to figure this out on your own before I work through it. So this first step, let's see. She got rid of this 2 by dividing the left-hand side by 2, and she appropriately divided.
Well, you can't just do that to one side. You have to do that to both sides in order to hold this equality. So she divided 242 by 2 as well, so that is correct. Step one makes sense. And then she just wanted-- instead of this being an x plus 4 squared, she wanted it to be an x plus 4.
So she attempted to take the square root of both sides. She said hey, look. The square root of x plus 4 squared is x plus 4, and the square root of 121 is 11. And this is where she made a small but very, very, very, very important mistake. Because if something squared is equal to 121, that means that something could be the positive or negative square root of 121.
This thing that we're squaring could be positive 11, because positive 11 squared is 121, or x plus 4 right over here could be negative 11, because negative 11 squared is also 121. So this right over here, this should say x plus 4 is equal to the positive or negative square root of 11, and so that's why she missed out on one of the solutions right over here.
So she messed up in step two. She should have taken the positive and negative square root. So, we got that right.
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