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# Solving quadratics by taking square roots: with steps

Video 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.