Solve -2x2 +3x - 9 = 0

Question

anonymous · Answer

hey @sam15389

anonymous · Answer

There are more than just one solution for this problem would you like both of them?

raffle_snaffle · Answer

do you have a ti-89

raffle_snaffle · Answer

do you have to justify your answer?

anonymous · Answer

First you have to simplify:  x2+3x  -  9

raffle_snaffle · Answer

I fanned you because you don't give the answer away.=)

anonymous · Answer

That's one thing I try my best never to do :D

raffle_snaffle · Answer

Sometimes they trick you! Lol

anonymous · Answer

Then you have to factor it out: $$x2+3x-9$$   

The first term is,  x2  its coefficient is  1, the middle term is,  +3x  its coefficient is  3, the last term, "the constant", is  -9 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -9 = -9 

Step-2 : Find two factors of  -9  whose sum equals the coefficient of the middle term, which is   3 .

     	-9	   +   	1	   =   	-8	
     	-3	   +   	3	   =   	0	
     	-1	   +   	9	   =   	8

anonymous · Answer

-2x2 +3x - 9 = 0
-4-9=-3x
-13=-3x
x=13/3

When you have a variable you don't want to deal with right a way just set it aside as I did.
Then deal with what you can in front of you.
After you've simplified your left side clean up both sides to solve for what you desired.

anonymous · Answer

depending on where you end up and how you perform through the succeeding steps then you will end up with one of two or both solutions

radar · Answer

Use the quadratic formula.  The two roots are complex containing both real and imaginary values.

campbell_st · Answer

why not just use the general quadratic formula given the quadratic has no real roots. The discriminant < 0

jhannybean · Answer

Here's a tricky method to solve it, but it's still fun nonetheless.
$$-2x^2 +3x -9=0$$Multiply your entire equation by -1$$2x^2 -3x+9=0$$Divide entire equation by 2 to get it in it's simplest form$$x^2 -\frac{3}{2}x +\frac{9}{2}=0$$Now we complete the square. $$\left( x^2 -\frac{3}{2}x\right)+\frac{9}{2} =0$$$$\left(x^2 -\frac{3}{2}x +\frac{9}{16}\right) +\frac{9}{2} -\frac{9}{16}=0$$$$\left( x-\frac{3}{4}\right)^2 +\frac{63}{16}=0$$$$\left(x-\frac{3}{4}\right)^2=-\frac{63}{16}$$$$x-\frac{3}{4} =\pm \sqrt{-\frac{63}{16}}$$$$x= \frac{3}{4} \pm \sqrt{-\frac{63}{16}}$$

jhannybean · Answer

$$x = \frac{3}{4} +i\frac{3\sqrt{7}}{4} \ ,\ \frac{3}{4}-i\frac{3\sqrt{7}}{4}$$

radar · Answer

Yes, completing the square is a practical way to solve it.  In fact completing the square is one method to develop the "quadratic formula"