SOLUTION: solve and express your answers in simplest a+bi form. (x squared/4)=x-2 i tried to put all the x's on one side and i got -x squared+x-8 i have no idea if thats right and if it

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: solve and express your answers in simplest a+bi form. (x squared/4)=x-2 i tried to put all the x's on one side and i got -x squared+x-8 i have no idea if thats right and if it       Log On


   

Question 252071: solve and express your answers in simplest a+bi form.
(x squared/4)=x-2 i tried to put all the x's on one side and
i got -x squared+x-8 i have no idea if thats right and if it is
i dont know where to go from there
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2F4=x-2 Start with the given equation.


x%5E2=4%28x-2%29 Multiply both sides by 4.


x%5E2=4x-8 Distribute.


x%5E2-4x%2B8=0 Get every term to the left side.


Notice that the quadratic x%5E2-4x%2B8 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-4, and C=8


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%281%29%288%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-4, and C=8


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%288%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%281%29%288%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-32+%29%29%2F%282%281%29%29 Multiply 4%281%29%288%29 to get 32


x+=+%284+%2B-+sqrt%28+-16+%29%29%2F%282%281%29%29 Subtract 32 from 16 to get -16


x+=+%284+%2B-+sqrt%28+-16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%284+%2B-+4%2Ai%29%2F%282%29 Take the square root of -16 to get 4%2Ai.


x+=+%284+%2B+4%2Ai%29%2F%282%29 or x+=+%284+-+4%2Ai%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29+%2B+%284%2Ai%29%2F%282%29 or x+=++%284%29%2F%282%29+-+%284%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+2%2B2%2Ai or x+=++2-2%2Ai Reduce.


x+=+2%2B2%2Ai or x+=+2-2%2Ai Simplify.


So the solutions are x+=+2%2B2%2Ai or x+=+2-2%2Ai