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Solving an Equation by Taking the Square Root

Part 1

In this video, we are going to look at solving equations by taking the square root.
For example:
If we are given the equation
x^2=9
we can solve for x by taking the square root of both sides.
\sqrt{x^2}=\sqrt{9}
This will leave us with just x. However, the square root of 9 isn’t just 3. It can be positive or negative 3. So
x=\pm{3}
If we had something more complicated like
x^2-5=31
then we would first have to get the x^2 by itself. So, first add 5 to both sides to isolate the x^2. Now we are left with x^2=36. Then take the square root of both sides
\sqrt{x^2}=\sqrt{36}
x=\pm6

Part 2

In this video, we are going to look at solving equations by taking the square root more in depth.
For example:
If we are given the equation
(x+5)^2=9
we can first take the square root of both sides.
\sqrt{(x+5)^2}=\sqrt{9}
This will leave us with
x+5=\pm{3}
Then subtract 5 from both sides and get
x=-5+3 and x=-5-3
This leads us to a final answer of
x=-2,-8
If we had something more complicated like
(x+2)^2-3=13
then we would first have to get the (x+2)^2 by itself. So, first add 3 to both sides to isolate the (x+2)^2. Now we are left with (x+2)^2=16. Then take the square root of both sides
\sqrt{(x+2)^2}=\sqrt{16}
x+2=\pm4
Subtract 2 from both sides
x=-2\pm4
x=-2+4 and x=-2-4
So
x=2,-6

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