SOLUTION: Solve using quadratic formula. 5x^2-x+3=0

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Question 96724: Solve using quadratic formula.
5x^2-x+3=0
Found 2 solutions by jim_thompson5910, checkley71:
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 5%2Ax%5E2-x%2B3=0 ( notice a=5, b=-1, and c=3)

x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A5%2A3+%29%29%2F%282%2A5%29 Plug in a=5, b=-1, and c=3



x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A5%2A3+%29%29%2F%282%2A5%29 Negate -1 to get 1



x+=+%281+%2B-+sqrt%28+1-4%2A5%2A3+%29%29%2F%282%2A5%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)



x+=+%281+%2B-+sqrt%28+1%2B-60+%29%29%2F%282%2A5%29 Multiply -4%2A3%2A5 to get -60



x+=+%281+%2B-+sqrt%28+-59+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)



x+=+%281+%2B-+i%2Asqrt%2859%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%281+%2B-+i%2Asqrt%2859%29%29%2F%2810%29 Multiply 2 and 5 to get 10



After simplifying, the quadratic has roots of

x=1%2F10+%2B+sqrt%2859%29%2F10%2Ai or x=1%2F10+-+sqrt%2859%29%2F10%2Ai

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

+graph%28+500%2C+500%2C+-14.9%2C+15.1%2C+-12.05%2C+17.95%2C+5%2Ax%5E2-x%2B3%29+ graph of y=5%2Ax%5E2-x%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

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2-x+3=0
x+=+%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(1+-sqrt[-1^2-4*5*3])/2*5
x=(1+-sqrt[1-60])/10
x=(1+-sqrt-59)/10
x=(1+-7.68i)/10
x=1/10+7.68i/10
x=.1+.768i answer.
x=(1-7.68i)/10
x=.1-.768i answer.