SOLUTION: Solve by using quadratic formula 4x^2-3x+3=0

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Question 113718This question is from textbook Beginning Algebra
: Solve by using quadratic formula
4x^2-3x+3=0 This question is from textbook Beginning Algebra

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 4%2Ax%5E2-3%2Ax%2B3=0 ( notice a=4, b=-3, and c=3)




x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A3+%29%29%2F%282%2A4%29 Plug in a=4, b=-3, and c=3



x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A3+%29%29%2F%282%2A4%29 Negate -3 to get 3



x+=+%283+%2B-+sqrt%28+9-4%2A4%2A3+%29%29%2F%282%2A4%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)



x+=+%283+%2B-+sqrt%28+9%2B-48+%29%29%2F%282%2A4%29 Multiply -4%2A3%2A4 to get -48



x+=+%283+%2B-+sqrt%28+-39+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)



x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%288%29 Multiply 2 and 4 to get 8



After simplifying, the quadratic has roots of

x=3%2F8+%2B+sqrt%2839%29%2F8%2Ai or x=3%2F8+-+sqrt%2839%29%2F8%2Ai

Notice if we graph the quadratic y=4%2Ax%5E2-3%2Ax%2B3, we get

+graph%28+500%2C+500%2C+-14.625%2C+15.375%2C+-12.5625%2C+17.4375%2C+4%2Ax%5E2-3%2Ax%2B3%29+ graph of y=4%2Ax%5E2-3%2Ax%2B3

And we can see that there are no real roots

To visually verify the answer, check out this page to see a visual representation of imaginary roots