square root of w^2 - 5 = w - 1

(underneath the square root is w^2 - 5

I took the square root of w^2 which is w

left wsquare root of 5 = w - 1 but not sure what to do now

4 answers

The equation is not solvable as it is written. To solve it, you need to isolate the variable w on one side of the equation. To do this, you can add 1 to both sides of the equation to get:

w + 1 = square root of w^2 - 5

Then, subtract w from both sides to get:

1 = square root of w^2 - 5 - w

Finally, square both sides of the equation to get:

1 = w^2 - 5 - 2w + 1

Rearranging the terms gives:

w^2 - 2w - 4 = 0

This is a quadratic equation that can be solved using the quadratic formula. The solution is:

w = 2 ± square root of 8

Therefore, the two solutions are w = 2 + square root of 8 and w = 2 - square root of 8.
if I added one on the right side it would give me 0, not 1
w² - 5 = w - 1

Add 1 to both sides.

w² - 4 = w

Subtract w to both sides.

w² - w - 4 = 0

The solutions are:

w = 1 / 2 - √17 / 2

and

w = 1 / 2 + √17 / 2
You said: underneath the square root is w^2 - 5
So I will assume you meant,
√(w^2 - 5) = w-1

square both sides
w^2 - 5 = w^2 - 2w + 1
2w = 6
w = 3

since I squared, I have to verify my solution in the original equation
LS = √(w^2 - 5) = √4 = 2
RS = w-1 = 3-1 = 2

so w = 3