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Explain why the equation (x-4)^2-10=15 has two solutions. Then solve the equation to find the solutions.

Please show all your work! (30 points)

1 Answer

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Hello there,
Let's solve it first so that we can understand whats going on in the equation

(x-4)²-10=15
add 10 to both sides
(x-4)²=25
square root both sides

(Okay, so here is where the problem can have 2 solutions. Because the square root of 25 could be (5*5) or it could be (-5*-5). If it's positive five then...

x-4=5
add 4 to both sides
x=9

if it's negative 5 then...

x-4=-5
add 4 to both sides
x=-1

So the answer could be x=-1 or x=9.

It has two solutions because there are two possibilities for the answer to the square root of 25.

I hope this help, and if you have any more questions, please feel free to ask me.
Have a nice day!

User Andi North
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