SOLUTION: very confused about these two questions solve for x x(x - 5) =4 and (x +2))x-3)(x-6)=0 thanks for your help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: very confused about these two questions solve for x x(x - 5) =4 and (x +2))x-3)(x-6)=0 thanks for your help.      Log On


   

Question 21675: very confused about these two questions
solve for x
x(x - 5) =4
and
(x +2))x-3)(x-6)=0
thanks for your help.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1st: x^2-5x=4
x^2-5x-4=0
Use the quadratic formula to get:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B-4+=+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=%28-5%29%5E2-4%2A1%2A-4=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+41+%29%29%2F2%5C1+=+5.70156211871642
x%5B2%5D+=+%28-%28-5%29-sqrt%28+41+%29%29%2F2%5C1+=+-0.701562118716424

Quadratic expression 1x%5E2%2B-5x%2B-4 can be factored:
1x%5E2%2B-5x%2B-4+=+1%28x-5.70156211871642%29%2A%28x--0.701562118716424%29
Again, the answer is: 5.70156211871642, -0.701562118716424. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-4+%29

2nd:
(x+2)(x-3)(x-6)=0
For this product to be zero one of these factors must be zero, so:
x+2=0 or x-3=0 or x-6=0
So, x=-2 or x=3 or x=6
Cheers,
Stan H.