SOLUTION: -6z2(squared)+7z+3=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: -6z2(squared)+7z+3=0      Log On


   

Question 206893This question is from textbook Elementary and Intermediate
: -6z2(squared)+7z+3=0 This question is from textbook Elementary and Intermediate

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

-6z%5E2%2B7z%2B3=0 Start with the given equation.


Notice that the quadratic -6z%5E2%2B7z%2B3 is in the form of Az%5E2%2BBz%2BC where A=-6, B=7, and C=3


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-%287%29+%2B-+sqrt%28+%287%29%5E2-4%28-6%29%283%29+%29%29%2F%282%28-6%29%29 Plug in A=-6, B=7, and C=3


z+=+%28-7+%2B-+sqrt%28+49-4%28-6%29%283%29+%29%29%2F%282%28-6%29%29 Square 7 to get 49.


z+=+%28-7+%2B-+sqrt%28+49--72+%29%29%2F%282%28-6%29%29 Multiply 4%28-6%29%283%29 to get -72


z+=+%28-7+%2B-+sqrt%28+49%2B72+%29%29%2F%282%28-6%29%29 Rewrite sqrt%2849--72%29 as sqrt%2849%2B72%29


z+=+%28-7+%2B-+sqrt%28+121+%29%29%2F%282%28-6%29%29 Add 49 to 72 to get 121


z+=+%28-7+%2B-+sqrt%28+121+%29%29%2F%28-12%29 Multiply 2 and -6 to get -12.


z+=+%28-7+%2B-+11%29%2F%28-12%29 Take the square root of 121 to get 11.


z+=+%28-7+%2B+11%29%2F%28-12%29 or z+=+%28-7+-+11%29%2F%28-12%29 Break up the expression.


z+=+%284%29%2F%28-12%29 or z+=++%28-18%29%2F%28-12%29 Combine like terms.


z+=+-1%2F3 or z+=+3%2F2 Simplify.


So the solutions are z+=+-1%2F3 or z+=+3%2F2