What is the answer to (x-sqrt(x-1))^2=169 ?

The answer to (x-sqrt(x-1))^2=169 is x=17

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(x-sqrt(x-1))^2=169

(x - x - 1)^{2} = 169

x = 17

Solution steps

(x - x - 1)^{2} = 169

Move

169

to the left side

(x - x - 1)^{2} - 169 = 0

Factor

(x - x - 1)^{2} - 169 : (x - x - 1 + 13) (x - x - 1 - 13)

(x - x - 1 + 13) (x - x - 1 - 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - x - 1 + 13 = 0 or x - x - 1 - 13 = 0

Solve

x - x - 1 + 13 = 0 :

No Solution for

x \in R

Solve

x - x - 1 - 13 = 0 : x = 17

x = 17

Verify Solutions:

x = 17

True

The solution is

x = 17

x + 1 + 1 = x + 3

3 - 11 x = x + 9

x^{2} + 2 x + 3 = 0

(x - 0)^{2} + (- x - 0)^{2} = 1

What is the answer to (x-sqrt(x-1))^2=169 ?
The answer to (x-sqrt(x-1))^2=169 is x=17
Solve for x: (x-sqrt(x-1))^2=169
The solution is x=17