SOLUTION: Solve by quadratic Equation. 3x^2-6x+2=0 Please explain.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve by quadratic Equation. 3x^2-6x+2=0 Please explain.      Log On


   

Question 89197: Solve by quadratic Equation.
3x^2-6x+2=0
Please explain.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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%5E2-6%2Ax%2B2=0 ( notice a=3, b=-6, and c=2)

x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29 Plug in a=3, b=-6, and c=2



x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29 Negate -6 to get 6



x+=+%286+%2B-+sqrt%28+36-4%2A3%2A2+%29%29%2F%282%2A3%29 Square -6 to get 36



x+=+%286+%2B-+sqrt%28+36%2B-24+%29%29%2F%282%2A3%29 Multiply -4%2A2%2A3 to get -24



x+=+%286+%2B-+sqrt%28+12+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%286+%2B-+2%2Asqrt%283%29%29%2F%282%2A3%29 Simplify the square root



x+=+%286+%2B-+2%2Asqrt%283%29%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%286+%2B+2%2Asqrt%283%29%29%2F6 or x+=+%286+-+2%2Asqrt%283%29%29%2F6


which split up to


x=%2B6%2F6%2B2%2Asqrt%283%29%2F6 or x=%2B6%2F6-2%2Asqrt%283%29%2F6


and simplify to


x=1%2Bsqrt%283%29%2F+3 or x=1-sqrt%283%29%2F+3


Which approximate to

x=1.57735026918963 or x=0.422649730810374


So our solutions are:
x=1.57735026918963 or x=0.422649730810374

Notice when we graph 3%2Ax%5E2-6%2Ax%2B2, we get:



when we use the root finder feature on a calculator, we find that x=1.57735026918963 and x=0.422649730810374.So this verifies our answer