SOLUTION: Can you please show me how to work this problem out, I am having trouble w / it. Solve the equation using the quadratic formula 1 = 3q^2 + 4q Thank you so very much

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can you please show me how to work this problem out, I am having trouble w / it. Solve the equation using the quadratic formula 1 = 3q^2 + 4q Thank you so very much      Log On


   

Question 169982: Can you please show me how to work this problem out, I am having trouble w / it.
Solve the equation using the quadratic formula
1 = 3q^2 + 4q
Thank you so very much
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1+=+3q%5E2+%2B+4q Start with the given equation


0+=+3q%5E2+%2B+4q-1 Subtract 1 from both sides.


Notice we have a quadratic equation in the form of aq%5E2%2Bbq%2Bc where a=3, b=4, and c=-1


Let's use the quadratic formula to solve for q


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


q+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%283%29%28-1%29+%29%29%2F%282%283%29%29 Plug in a=3, b=4, and c=-1


q+=+%28-4+%2B-+sqrt%28+16-4%283%29%28-1%29+%29%29%2F%282%283%29%29 Square 4 to get 16.


q+=+%28-4+%2B-+sqrt%28+16--12+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-1%29 to get -12


q+=+%28-4+%2B-+sqrt%28+16%2B12+%29%29%2F%282%283%29%29 Rewrite sqrt%2816--12%29 as sqrt%2816%2B12%29


q+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%282%283%29%29 Add 16 to 12 to get 28


q+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


q+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


q+=+%28-4%2B2%2Asqrt%287%29%29%2F%286%29 or q+=+%28-4-2%2Asqrt%287%29%29%2F%286%29 Break up the expression.


So the answers are q+=+%28-4%2B2%2Asqrt%287%29%29%2F%286%29 or q+=+%28-4-2%2Asqrt%287%29%29%2F%286%29


which approximate to q=0.215 or q=-1.549