SOLUTION: Solve for z: z^2-2z+1=-4

Question 139800: Solve for z: z^2-2z+1=-4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Add 4 to both sides.

Combine like terms

Let's use the quadratic formula to solve for z:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-2, and c=5

Negate -2 to get 2

Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

After simplifying, the quadratic has roots of

or

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