SOLUTION: use the quadratic formula to solve z^2-8z=-5

You can put this solution on YOUR website!


Add 5 to both sides

Now 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=-8, and c=5



Negate -8 to get 8



Square -8 to get 64



Multiply to get



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



Simplify the square root



Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or


Which approximate to

or


So our solutions are:
or

Notice when we graph (just replace z with x), we get:



when we use the root finder feature on a calculator, we find that and .So this verifies our answer