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

Question 88512: use the quadratic formula to solve z^2-8z=-5
Answer by jim_thompson5910(35256) (Show Source): 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
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