SOLUTION: Hi I have several questions that I completely don’t understand and need help on. 1. Solve by completing the square y^2-6y=16 2. Determine the nature of the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi I have several questions that I completely don’t understand and need help on. 1. Solve by completing the square y^2-6y=16 2. Determine the nature of the       Log On


   

Question 52064: Hi I have several questions that I completely don’t understand and need help on.

1. Solve by completing the square y^2-6y=16





2. Determine the nature of the solutions of 3z^2+2z-1=0





3. Solve Using the quadratic formula 3p^2-3p-4=0


4. Solve 2x^2-5x-12=0



I would really appreciate if you could help me with these problems as soon as possible because I have a test and I need some help so it would be nice if you could respond before 7 am tomorrow morning.
Thanks,
Jake
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2-6y=16
y%5E2+-6y+%2B+9+=+16+%2B+9
%28y+-+3%29%5E2+=+25
What I did was take 1/2 of the coefficient of y, square it, and add it to
both sides
y+-+3+=+5
y+=+8
check
y%5E2-6y=16
8%5E2+-6%2A8+=+16
64+-+48+=+16
16+=+16
OK
------------------
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
If b^2-4*a*c turns out to be positive, then the solutions are real
If it's negative, the solutions are imaginary
-------
3p^2-3p-4=0
p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
p+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A3%2A%28-4%29+%29%29%2F%282%2A3%29+
p+=+%283+%2B-+sqrt%2857+%29%29%2F6+ answer
------
2x^2-5x-12=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%285+%2B-+sqrt%28+25-96+%29%29%2F4+
x+=+%285+%2B-+sqrt%28+121+%29%29%2F4+
x+=+%285+%2B+11%29%2F+4
x+=+%285+-+11%29%2F+4
So the solutions are x = 4, x = - 3/2