SOLUTION: Solve the equation 8x^2-10x+3=0. x=?

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Question 115250: Solve the equation 8x^2-10x+3=0. x=?
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 8%2Ax%5E2-10%2Ax%2B3=0 ( notice a=8, b=-10, and c=3)




x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A8%2A3+%29%29%2F%282%2A8%29 Plug in a=8, b=-10, and c=3



x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A8%2A3+%29%29%2F%282%2A8%29 Negate -10 to get 10



x+=+%2810+%2B-+sqrt%28+100-4%2A8%2A3+%29%29%2F%282%2A8%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)



x+=+%2810+%2B-+sqrt%28+100%2B-96+%29%29%2F%282%2A8%29 Multiply -4%2A3%2A8 to get -96



x+=+%2810+%2B-+sqrt%28+4+%29%29%2F%282%2A8%29 Combine like terms in the radicand (everything under the square root)



x+=+%2810+%2B-+2%29%2F%282%2A8%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%2810+%2B-+2%29%2F16 Multiply 2 and 8 to get 16

So now the expression breaks down into two parts

x+=+%2810+%2B+2%29%2F16 or x+=+%2810+-+2%29%2F16

Lets look at the first part:

x=%2810+%2B+2%29%2F16

x=12%2F16 Add the terms in the numerator
x=3%2F4 Divide

So one answer is
x=3%2F4



Now lets look at the second part:

x=%2810+-+2%29%2F16

x=8%2F16 Subtract the terms in the numerator
x=1%2F2 Divide

So another answer is
x=1%2F2

So our solutions are:
x=3%2F4 or x=1%2F2

Notice when we graph 8%2Ax%5E2-10%2Ax%2B3, we get:

+graph%28+500%2C+500%2C+-9%2C+13%2C+-9%2C+13%2C8%2Ax%5E2%2B-10%2Ax%2B3%29+

and we can see that the roots are x=3%2F4 and x=1%2F2. This verifies our answer