SOLUTION: Solve equation by using the quadratic formula. 9x^2+5x-11=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve equation by using the quadratic formula. 9x^2+5x-11=0       Log On


   

Question 249185: Solve equation by using the quadratic formula.
9x^2+5x-11=0
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
9x^2+5x-11=0
--------------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B5x%2B-11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A9%2A-11=421.

Discriminant d=421 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+421+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+421+%29%29%2F2%5C9+=+0.862126918260177
x%5B2%5D+=+%28-%285%29-sqrt%28+421+%29%29%2F2%5C9+=+-1.41768247381573

Quadratic expression 9x%5E2%2B5x%2B-11 can be factored:
9x%5E2%2B5x%2B-11+=+%28x-0.862126918260177%29%2A%28x--1.41768247381573%29
Again, the answer is: 0.862126918260177, -1.41768247381573. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B5%2Ax%2B-11+%29

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

9x%5E2%2B5x-11=0 Start with the given equation.


Notice that the quadratic 9x%5E2%2B5x-11 is in the form of Ax%5E2%2BBx%2BC where A=9, B=5, and C=-11


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-%285%29+%2B-+sqrt%28+%285%29%5E2-4%289%29%28-11%29+%29%29%2F%282%289%29%29 Plug in A=9, B=5, and C=-11


x+=+%28-5+%2B-+sqrt%28+25-4%289%29%28-11%29+%29%29%2F%282%289%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--396+%29%29%2F%282%289%29%29 Multiply 4%289%29%28-11%29 to get -396


x+=+%28-5+%2B-+sqrt%28+25%2B396+%29%29%2F%282%289%29%29 Rewrite sqrt%2825--396%29 as sqrt%2825%2B396%29


x+=+%28-5+%2B-+sqrt%28+421+%29%29%2F%282%289%29%29 Add 25 to 396 to get 421


x+=+%28-5+%2B-+sqrt%28+421+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%28-5%2Bsqrt%28421%29%29%2F%2818%29 or x+=+%28-5-sqrt%28421%29%29%2F%2818%29 Break up the expression.


So the solutions are x+=+%28-5%2Bsqrt%28421%29%29%2F%2818%29 or x+=+%28-5-sqrt%28421%29%29%2F%2818%29


which approximate to x=0.862 or x=-1.418