SOLUTION: Solve using the quadratic formula please: Please help me with step by step instructions to help me understand. Thank you in advance! C

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Question 119765: Solve using the quadratic formula please:


Please help me with step by step instructions to help me understand.
Thank you in advance!
C
Found 3 solutions by Caallen2, jim_thompson5910, madhan_math:
Answer by Caallen2(9) About Me  (Show Source):
You can put this solution on YOUR website!
To begin you need to make one side equal to zero to get the total equation so you can solve for x.
3x^2-2x = 15x-10
subtract 15x and -10 from both sides
3x^2 - 2x - 15x - (-10)= 15x - 10 - 15x - (-10)
Simplify
3x^2 - 17x +10 = 0
Now you will break down this equation into two simpler equations. To do this you must determine which factors are needed. For example we know that 3's factors are only 3 and 1, however for 10 the factors are either 10 and 1 or 5 and 2. To determine which of these two to use you must look to the middle number, which is 17x. The factors that would make - 17x would be - 5 and -2 where 5 is going to be the factor that is multipled by 3x and 2 is the factor being multiplied by 1x.
(3x - 2)(x - 5) = 0
3x - 2 = 0 and x - 5 = 0
start with 3x - 2 = 0
add 2 to both sides
3x - 2 + 2 = 0 + 2
3x = 2
divide both sides by 3
3x/3 = 2/3
x = 2/3
now for the second part
x - 5 = 0
add 5 to both sides
x - 5 + 5 = 0 + 5
x = 5
So your solution will be x = 2/3, 5
To check your solution plug one of the answers for x into your orginal equation and solve.

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 madhan_math(34) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2-2x=15x-10.
Solution:
you rearrange the equation into the form 3x(x)-2(x)and then you take (x)=5.
This implies that 3x^2-2x=15x-10