SOLUTION: solve the equation (3m-6)^2 + 3(3m-6)-10=0 Thank you

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve the equation (3m-6)^2 + 3(3m-6)-10=0 Thank you      Log On


   

Question 242799: solve the equation
(3m-6)^2 + 3(3m-6)-10=0
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283m-6%29%5E2+%2B+3%283m-6%29-10=0 Start with the given equation.


Let z=3m-6


z%5E2+%2B+3z-10=0 Replace each '3m-6' with 'z'


Notice that the quadratic z%5E2%2B3z-10 is in the form of Az%5E2%2BBz%2BC where A=1, B=3, and C=-10


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-%283%29+%2B-+sqrt%28+%283%29%5E2-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Plug in A=1, B=3, and C=-10


z+=+%28-3+%2B-+sqrt%28+9-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Square 3 to get 9.


z+=+%28-3+%2B-+sqrt%28+9--40+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-10%29 to get -40


z+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F%282%281%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


z+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 9 to 40 to get 49


z+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


z+=+%28-3+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


z+=+%28-3+%2B+7%29%2F%282%29 or z+=+%28-3+-+7%29%2F%282%29 Break up the expression.


z+=+%284%29%2F%282%29 or z+=++%28-10%29%2F%282%29 Combine like terms.


z+=+2 or z+=+-5 Simplify.


So the solutions in terms of z are z+=+2 or z+=+-5

Since z=3m-6, this means that 3m-6=2 or 3m-6=-5. Solving for 'm' gets us the final solutions


m=8%2F3 or m=1%2F3