SOLUTION: (x+4)(x-9)=4x How do I solve this? step by step directions please? Thank you in advance.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (x+4)(x-9)=4x How do I solve this? step by step directions please? Thank you in advance.      Log On


   

Question 985345: (x+4)(x-9)=4x How do I solve this? step by step directions please?
Thank you in advance.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B4%29%28x-9%29+=+4x expand the left side
x%5E2+-9x+%2B4x+-36+=+4x combine lie terms
x%5E2+-5x+-+36+=+4x now solve
x%5E2+-9x+-36+=+0
Now either factor of use the quadratic equation.
Let's factor
what two integers have the sum -9 and the product of -36?
How about -12 and 3?
%28x-12%29%28x%2B3%29+=+0
For a product to equality zero, either one of both of its multiplicand or multiplier must be 0.
So either (x-12=0) or (x+3=0)
That says x = 12 or -3
Now lets use the quadratic equation to solve
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-9x%2B-36+=+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=%28-9%29%5E2-4%2A1%2A-36=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+225+%29%29%2F2%5C1+=+12
x%5B2%5D+=+%28-%28-9%29-sqrt%28+225+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-9x%2B-36 can be factored:
1x%5E2%2B-9x%2B-36+=+1%28x-12%29%2A%28x--3%29
Again, the answer is: 12, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B-36+%29


Either way, same result. Math is great!