SOLUTION: Can you please explain this to me? Solve using the quadratic formula 3x^2 - 2x = 15x - 10 thank you julie

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can you please explain this to me? Solve using the quadratic formula 3x^2 - 2x = 15x - 10 thank you julie      Log On


   

Question 118222: Can you please explain this to me?
Solve using the quadratic formula
3x^2 - 2x = 15x - 10
thank you
julie
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-2x=15x-10 Start with the given equation


3x%5E2-2x-15x%2B10=0 Subtract 15x from both sides. Add 10 to both sides.



3x%5E2-17x%2B10=0 Combine like terms


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%5E2-17%2Ax%2B10=0 ( notice a=3, b=-17, and c=10)




x+=+%28--17+%2B-+sqrt%28+%28-17%29%5E2-4%2A3%2A10+%29%29%2F%282%2A3%29 Plug in a=3, b=-17, and c=10



x+=+%2817+%2B-+sqrt%28+%28-17%29%5E2-4%2A3%2A10+%29%29%2F%282%2A3%29 Negate -17 to get 17



x+=+%2817+%2B-+sqrt%28+289-4%2A3%2A10+%29%29%2F%282%2A3%29 Square -17 to get 289 (note: remember when you square -17, you must square the negative as well. This is because %28-17%29%5E2=-17%2A-17=289.)



x+=+%2817+%2B-+sqrt%28+289%2B-120+%29%29%2F%282%2A3%29 Multiply -4%2A10%2A3 to get -120



x+=+%2817+%2B-+sqrt%28+169+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%2817+%2B-+13%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%2817+%2B-+13%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%2817+%2B+13%29%2F6 or x+=+%2817+-+13%29%2F6

Lets look at the first part:

x=%2817+%2B+13%29%2F6

x=30%2F6 Add the terms in the numerator
x=5 Divide

So one answer is
x=5



Now lets look at the second part:

x=%2817+-+13%29%2F6

x=4%2F6 Subtract the terms in the numerator
x=2%2F3 Divide

So another answer is
x=2%2F3

So our solutions are:
x=5 or x=2%2F3

Notice when we graph 3%2Ax%5E2-17%2Ax%2B10, we get:

+graph%28+500%2C+500%2C+-8%2C+15%2C+-8%2C+15%2C3%2Ax%5E2%2B-17%2Ax%2B10%29+

and we can see that the roots are x=5 and x=2%2F3. This verifies our answer