SOLUTION: Solve z^2+z=5

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Question 193133: Solve z^2+z=5


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

z%5E2%2Bz=5 Start with the given equation.


z%5E2%2Bz-5=0 Subtract 5 from both sides.


Notice we have a quadratic equation in the form of az%5E2%2Bbz%2Bc=0 where a=1, b=1, and c=-5


Let's use the quadratic formula to solve for z


z+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


z+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Plug in a=1, b=1, and c=-5


z+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


z+=+%28-1+%2B-+sqrt%28+1--20+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-5%29 to get -20


z+=+%28-1+%2B-+sqrt%28+1%2B20+%29%29%2F%282%281%29%29 Rewrite sqrt%281--20%29 as sqrt%281%2B20%29


z+=+%28-1+%2B-+sqrt%28+21+%29%29%2F%282%281%29%29 Add 1 to 20 to get 21


z+=+%28-1+%2B-+sqrt%28+21+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


z+=+%28-1%2Bsqrt%2821%29%29%2F%282%29 or z+=+%28-1-sqrt%2821%29%29%2F%282%29 Break up the expression.


So the answers are z+=+%28-1%2Bsqrt%2821%29%29%2F%282%29 or z+=+%28-1-sqrt%2821%29%29%2F%282%29


which approximate to z=1.791 or z=-2.791 (using a calculator)