Question

Solve (x-4)^2=25
What method was used?

Answer 1

When trying to solve for a variable a good place to start is to think about what was done to it. (Use PEDMAS)

In this problem:
1st: 4 was subtracted from x
2nd: x was squared

So to solve for x undo what was done to it. So do to x the opposite of what was done to it, but in reverse order. (Remember what you do to one side of the equal sign you have to do to another).

In this problem:
1st: square root x and square root 25 (this cancels out the square)
2nd: add 4 to x and add 4 to 25 (this cancels out the -4)

So simplified:
(X-4)^2=25
(X-4)=5
X=9

Answer 2

(x - 4)² = 25
x - 4 =
`\pm` √25
x - 4 =
`\pm` 5
x = 5 + 4 or x = -5 + 4
x = 9 or x = -1

Method Use : Completing the square

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Answer: x = 9 or x = -1
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