SOLUTION: Use factoring to solve this equation. (Here's a hint: Clear the parentheses first.) x(x + 7) = 4(3 + 2x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use factoring to solve this equation. (Here's a hint: Clear the parentheses first.) x(x + 7) = 4(3 + 2x)       Log On


   

Question 1036538: Use factoring to solve this equation. (Here's a hint: Clear the parentheses first.)
x(x + 7) = 4(3 + 2x)
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
hint means simple distribution or multiplying
x%5E2%2B7x=12%2B8x gather everything on left side so subtract 12 and 8x from both sides
x%5E2%2B7x-8x-12=0
x%5E2-x-12=0
several ways to solve this i chose the fast way which is finding two numbers that multiply to get -12 and add to get -1 these numbers come from: find 2 numbers that multiply to get c and add to get b in the quadratic equation formula ax%5E2%2Bbx%2Bc=0
a -4 and a 3 multiply to -12 and add to -1
%28x-4%29%28x%2B3%29=0
x= 4 , -3
if you cant get that trick down just do the long quadratic equation:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-12+=+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=%28-1%29%5E2-4%2A1%2A-12=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%28-1%29-sqrt%28+49+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-1x%2B-12 can be factored:
1x%5E2%2B-1x%2B-12+=+1%28x-4%29%2A%28x--3%29
Again, the answer is: 4, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-12+%29