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Question 1023131: Explain how to solve X=(y+2)2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i presume you mean exponentiation, which is modeled using the exponentiation symbol of ^.
based on that, x = (y+2)2 would be modeled as x = (y+2)^2.
assuming that's what you meant, then you would take the square root of both sides of the equation to get plus or minus sqrt(x) = y+2.
you would then subtract 2 from both sides of the equation to get plus or minus sqrt(x) - 2 = y.
this can also be shown as y = - 2 plus or minus sqrt(x).
to confirm that this is the equivalent of the original equation, then do the following:
start with y = -2 plus or minus sqrt(x).
add 2 to both sides of this equation to get y + 2 = plus or minus sqrt(xj).
square both sides of this equation to get (y+2)^2 = (sqrt(x))^2 or (-sqrt(x))^2.
in either case, you get (y+2)^2 = x.
when you deal with square roots, the following rules apply.
if the problem states that y^2 = 4, then the solution is y = plus or minus 2.
is the problem states that y = sqrt(4), then the solution is y = 2, not plus or minus 2.
it's a subtle difference that can be difficult to understand.
here's a reference that discusses it.
https://www.mathsisfun.com/algebra/square-root.html
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