SOLUTION: Simplify the equation, then solve by the quadratic formula. Use i notation for nonreal complex numbers. {{{3x^2 -4x+4=0}}} 3x^2 -4x = -4 (4/2)^2 = 4 3x^2+4 -4x= Now

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Simplify the equation, then solve by the quadratic formula. Use i notation for nonreal complex numbers. {{{3x^2 -4x+4=0}}} 3x^2 -4x = -4 (4/2)^2 = 4 3x^2+4 -4x= Now       Log On


   

Question 264732: Simplify the equation, then solve by the quadratic formula. Use i notation for nonreal complex numbers.
3x%5E2+-4x%2B4=0
3x^2 -4x = -4
(4/2)^2 = 4
3x^2+4 -4x=
Now I am confused!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-4x%2B4=0 Start with the given equation.


Notice that the quadratic 3x%5E2-4x%2B4 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-4, and C=4


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%283%29%284%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-4, and C=4


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%283%29%284%29+%29%29%2F%282%283%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%283%29%284%29+%29%29%2F%282%283%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-48+%29%29%2F%282%283%29%29 Multiply 4%283%29%284%29 to get 48


x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%282%283%29%29 Subtract 48 from 16 to get -32


x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%284+%2B-+4i%2Asqrt%282%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%284%2B4i%2Asqrt%282%29%29%2F%286%29 or x+=+%284-4i%2Asqrt%282%29%29%2F%286%29 Break up the expression.


x+=+%282%2B2i%2Asqrt%282%29%29%2F%283%29 or x+=+%282-2i%2Asqrt%282%29%29%2F%283%29 Reduce.


So the solutions are x+=+%282%2B2i%2Asqrt%282%29%29%2F%283%29 or x+=+%282-2i%2Asqrt%282%29%29%2F%283%29