SOLUTION: z^2+5z-14=0

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Question 106726: z^2+5z-14=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for z:


Starting with the general quadratic


az%5E2%2Bbz%2Bc=0


the general solution using the quadratic equation is:


z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve z%5E2%2B5%2Az-14=0 ( notice a=1, b=5, and c=-14)





z+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-14+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=-14




z+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-14+%29%29%2F%282%2A1%29 Square 5 to get 25




z+=+%28-5+%2B-+sqrt%28+25%2B56+%29%29%2F%282%2A1%29 Multiply -4%2A-14%2A1 to get 56




z+=+%28-5+%2B-+sqrt%28+81+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




z+=+%28-5+%2B-+9%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




z+=+%28-5+%2B-+9%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


z+=+%28-5+%2B+9%29%2F2 or z+=+%28-5+-+9%29%2F2


Lets look at the first part:


x=%28-5+%2B+9%29%2F2


z=4%2F2 Add the terms in the numerator

z=2 Divide


So one answer is

z=2




Now lets look at the second part:


x=%28-5+-+9%29%2F2


z=-14%2F2 Subtract the terms in the numerator

z=-7 Divide


So another answer is

z=-7


So our solutions are:

z=2 or z=-7