Question

Solve (x-7)^2 = 25 using square roots

Answer 1

(x-7)(x-7)=25

X^2-7x-7x+49=25

X^2-14x+49-25=0

X^2-14x+24=0

(x-12)(x-2)=0

Therefore x-12=0 or x-2=0

X=12. Or X=2

Answer 2

{2, 12}

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Given equation:

• (x - 7)² = 25

Note that 25 = 5². Then our equation becomes:

• (x - 7)² = 5²

Now square root both sides:

• 
  `√((x-7)^2) =√(5^2)`

It simplifies as:

• |x - 7| = 5

Which can be written as two equations:

• x - 7 = 5 or

• x - 7 = - 5

Then the solution is:

• x = 5 + 7 = 12 or

• x = - 5 + 7 = 2