SOLUTION: 3x2 -15x + 12 =

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Question 102753: 3x2 -15x + 12 =
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-15%2Ax%2B12=0 ( notice a=3, b=-15, and c=12)




x+=+%28--15+%2B-+sqrt%28+%28-15%29%5E2-4%2A3%2A12+%29%29%2F%282%2A3%29 Plug in a=3, b=-15, and c=12



x+=+%2815+%2B-+sqrt%28+%28-15%29%5E2-4%2A3%2A12+%29%29%2F%282%2A3%29 Negate -15 to get 15



x+=+%2815+%2B-+sqrt%28+225-4%2A3%2A12+%29%29%2F%282%2A3%29 Square -15 to get 225 (note: remember when you square -15, you must square the negative as well. This is because %28-15%29%5E2=-15%2A-15=225.)



x+=+%2815+%2B-+sqrt%28+225%2B-144+%29%29%2F%282%2A3%29 Multiply -4%2A12%2A3 to get -144



x+=+%2815+%2B-+sqrt%28+81+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%2815+%2B-+9%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%2815+%2B-+9%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%2815+%2B+9%29%2F6 or x+=+%2815+-+9%29%2F6

Lets look at the first part:

x=%2815+%2B+9%29%2F6

x=24%2F6 Add the terms in the numerator
x=4 Divide

So one answer is
x=4



Now lets look at the second part:

x=%2815+-+9%29%2F6

x=6%2F6 Subtract the terms in the numerator
x=1 Divide

So another answer is
x=1

So our solutions are:
x=4 or x=1

Notice when we graph 3%2Ax%5E2-15%2Ax%2B12, we get:

+graph%28+500%2C+500%2C+-9%2C+14%2C+-9%2C+14%2C3%2Ax%5E2%2B-15%2Ax%2B12%29+

and we can see that the roots are x=4 and x=1. This verifies our answer