Quadratics by taking square roots: strategy

Meredith is solving the following problem for homework 2 times the quantity X plus 4 squared is equal to 242 she completes the problem is 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 is x equals 7 and x equals negative 15 she only got x equals 7 year 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 to 42 by 2 as well so that is correct step one makes sense then she just wanted to instead of this being an X plus 4 squared she wanted 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 or or positive and negative square root so we got that right