SOLUTION: x^2+20=4x

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: x^2+20=4x      Log On


   

Question 185628: x^2+20=4x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B20=4x Start with the given equation.


x%5E2%2B20-4x=0 Subtract 4x from both sides.


x%5E2-4x%2B20=0 Rearrange the terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-4, and c=20


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%2820%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-4, and c=20


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%2820%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%281%29%2820%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-80+%29%29%2F%282%281%29%29 Multiply 4%281%29%2820%29 to get 80


x+=+%284+%2B-+sqrt%28+-64+%29%29%2F%282%281%29%29 Subtract 80 from 16 to get -64


x+=+%284+%2B-+sqrt%28+-64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%284+%2B-+8%2Ai%29%2F%282%29 Take the square root of -64 to get 8%2Ai.


x+=+%284+%2B+8%2Ai%29%2F%282%29 or x+=+%284+-+8%2Ai%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29+%2B+%288%2Ai%29%2F%282%29 or x+=++%284%29%2F%282%29+-+%288%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+2%2B4%2Ai or x+=++2-4%2Ai Reduce.


x+=+2%2B4%2Ai or x+=+2-4%2Ai Simplify.


So the answers are x+=+2%2B4%2Ai or x+=+2-4%2Ai