SOLUTION: Hello, I am having problems understanding the steps used to solve equations using the quadratic formula. Can you please show me detailed steps to understand how to solve this probl

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Question 118217: Hello, I am having problems understanding the steps used to solve equations using the quadratic formula. Can you please show me detailed steps to understand how to solve this problem. All help is greatly appreciated, thank you.
My directions say to use the quadratic formula to solve.
3x^2 – 2x = 15x – 10
Thank you
Patti
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
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

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
My directions say to use the quadratic formula to solve.
3x^2 – 2x = 15x – 10
:
The quadratic formula is based on the form ax^2 + bx + c = 0
:
Put your problem in that format:
3x^2 - 2x = 15x - 10
;
3x^2 - 2x - 15x = -10; subtract 15x from both sides
:
3x^2 -17x = -10; combined like terms
:
3x^2 -17x + 10 = 0; added 10 to both sides, this is format we want
:
In this problem a=3; b=-17; c=10
:
The quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
Substitute our values for a, b, and c
x+=+%28-%28-17%29+%2B-+sqrt%28-17%5E2+-+4+%2A+3+%2A+10+%29%29%2F%282%2A3%29+
:
x+=+%2817+%2B-+sqrt%28289+-+120%29%29%2F%286%29+; it's +17, minus a minus is plus
:
x+=+%2817+%2B-+sqrt%28169%29%29%2F6+
:
x+=+%2817+%2B-+13%29%2F6; found the square root of 169
:
Two solutions:
x+=+%2817+%2B+13%29%2F6;
x+=+30%2F6
x = +5
and
x+=+%2817+-+13%29%2F6;
x+=+4%2F6
x+=+%2B2%2F3
:
:
Check both solution in the original equation to make sure we did not make a mistake somewhere.
x = 5
3x^2 – 2x = 15x – 10
3(5^2) - 2(5) = 15(5) - 10
3(25) - 10 = 75 - 10; equality reigns, a good solution
and
x = 2%2F3
3(2/3)^2 - 2(2/3) = 15(2/3) - 10
3(4/9) - (4/3) = 10 - 10
(12/9) - (4/3) = 0; checks OK too
:
Could you follow this OK, Any questions?