SOLUTION: Solve for x: 4x^2+9x=9 please show work

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve for x: 4x^2+9x=9 please show work      Log On


   

Question 315566: Solve for x:
4x^2+9x=9
please show work
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2%2B9x=9 Start with the given equation.


4x%5E2%2B9x-9=0 Subtract 9 from both sides.


Notice that the quadratic 4x%5E2%2B9x-9 is in the form of Ax%5E2%2BBx%2BC where A=4, B=9, and C=-9


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%289%29+%2B-+sqrt%28+%289%29%5E2-4%284%29%28-9%29+%29%29%2F%282%284%29%29 Plug in A=4, B=9, and C=-9


x+=+%28-9+%2B-+sqrt%28+81-4%284%29%28-9%29+%29%29%2F%282%284%29%29 Square 9 to get 81.


x+=+%28-9+%2B-+sqrt%28+81--144+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-9%29 to get -144


x+=+%28-9+%2B-+sqrt%28+81%2B144+%29%29%2F%282%284%29%29 Rewrite sqrt%2881--144%29 as sqrt%2881%2B144%29


x+=+%28-9+%2B-+sqrt%28+225+%29%29%2F%282%284%29%29 Add 81 to 144 to get 225


x+=+%28-9+%2B-+sqrt%28+225+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-9+%2B-+15%29%2F%288%29 Take the square root of 225 to get 15.


x+=+%28-9+%2B+15%29%2F%288%29 or x+=+%28-9+-+15%29%2F%288%29 Break up the expression.


x+=+%286%29%2F%288%29 or x+=++%28-24%29%2F%288%29 Combine like terms.


x+=+3%2F4 or x+=+-3 Simplify.


So the solutions are x+=+3%2F4 or x+=+-3