SOLUTION: Thank you for helping. I am trying to help my son with his final review. Solve: -3X^2-5x=4 There are no further directions, such as a method to use

Algebra ->  College  -> Linear Algebra -> SOLUTION: Thank you for helping. I am trying to help my son with his final review. Solve: -3X^2-5x=4 There are no further directions, such as a method to use      Log On


   

Question 117601: Thank you for helping. I am trying to help my son with his final review.
Solve: -3X^2-5x=4
There are no further directions, such as a method to use
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-3x%5E2-5x=4 Start with the given equation


-3x%5E2-5x-4=0 Subtract 4 from both sides


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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve -3%2Ax%5E2-5%2Ax-4=0 ( notice a=-3, b=-5, and c=-4)




x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A-3%2A-4+%29%29%2F%282%2A-3%29 Plug in a=-3, b=-5, and c=-4



x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A-3%2A-4+%29%29%2F%282%2A-3%29 Negate -5 to get 5



x+=+%285+%2B-+sqrt%28+25-4%2A-3%2A-4+%29%29%2F%282%2A-3%29 Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because %28-5%29%5E2=-5%2A-5=25.)



x+=+%285+%2B-+sqrt%28+25%2B-48+%29%29%2F%282%2A-3%29 Multiply -4%2A-4%2A-3 to get -48



x+=+%285+%2B-+sqrt%28+-23+%29%29%2F%282%2A-3%29 Combine like terms in the radicand (everything under the square root)



x+=+%285+%2B-+i%2Asqrt%2823%29%29%2F%282%2A-3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%285+%2B-+i%2Asqrt%2823%29%29%2F%28-6%29 Multiply 2 and -3 to get -6



After simplifying, the quadratic has roots of
x+=+%285+%2B+i%2Asqrt%2823%29%29%2F%28-6%29 or x+=+%285+-+i%2Asqrt%2823%29%29%2F%28-6%29