Answer:
Nice! Quadratic Equations!
Step-by-step explanation:
Okay, I'll try to keep it as brief as possible.
To find out how many solutions there are in a quadratic equation, we need to find the Discriminate.
It's pretty simple. The form of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
Our Discriminant is [tex]b^2-4ac[/tex].
Time to solve! (input b=7, a=9, and c=-4)
[tex]49+144\\193[/tex]
The discriminate is positive, meaning there are two answers.
If it was zero, there would be only one.
if it was negative, there would be no solutions.
Time to actually solve!
Completing the square looks to be a bad solution, so I'll go with the Quadratic Equation. Remember, don't use it too often.
(Quadratic Equation: [tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex])
[tex]x=\frac{-7+-\sqrt{49+144} }{18}[/tex]
[tex]x=\frac{-7+-\sqrt{193} }{18}[/tex] <-------SOLUTION! COME HERE!
193 seems to be a prime number, so I can't simplify it any more.
There's your solution!
(Note: +- means plus/minus, where there are two cases, one where the square root has a negative sign, and the other with a positive sign.)
Happy Quadraticing!
