(X-1)^-2=25

Question

It is a math problem and I have to solve for x in the equation

Answer 1

The exponent (-2) means that the left side of your equation is the reciprocal of the square of (x-1), so let's take the reciprocal of each side; now we have (x-1)² = 1/25.

 

Take square root of each side; that gives x-1 = ±1/5 so x = 1 ±1/5 = {4/5, 6/5}.

Answer 2

(x-1)^-2 = 25

 

(x-1)^-2 is the same as 1/(x-1)²

 

1/(x-1)²=25

 

1=25(x-1)²

 

1/25 = (x-1)²

 

1/5 = √(x-1)²

 

+ or - 1/5 = x-1

 

x-1 = 1/5 or x-1 = -1/5

 

x = 1 1/5 or x = 4/5