SOLUTION: 12. (8 pts) Consider the equation 4x2 + 25 = 12x. Find the complex solutions (real and non-real components) of the equation, and simplify as much as possible. Show work.

Algebra ->  Equations -> SOLUTION: 12. (8 pts) Consider the equation 4x2 + 25 = 12x. Find the complex solutions (real and non-real components) of the equation, and simplify as much as possible. Show work.       Log On


   

Question 1134679: 12. (8 pts) Consider the equation 4x2 + 25 = 12x. Find the complex solutions (real and non-real components) of the equation, and simplify as much as possible. Show work.




 
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2+%2B+25+=+12x

4x%5E2+-12x%2B+25+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A4%2A25+%29%29%2F%282%2A4%29+
x+=+%2812+%2B-+sqrt%28+144-400+%29%29%2F8+

x+=+%2812+%2B-+sqrt%28+-256+%29%29%2F8+

x+=+%2812+%2B-+sqrt%28256+%29sqrt%28+-1%29%29%2F8+

x+=+%2812+%2B-+16i%29%2F8+
x+=+%28cross%2812%293+%2B-+cross%2816%294i%29%2Fcross%288%292+

x+=+%283+%2B-+4i%29%2F2+


solutions:
x+=+%283+%2B+4i%29%2F2+ =>highlight%28x+=+3%2F2+%2B+2i+%29

x+=+%283+-+4i%29%2F2+ =>highlight%28x+=+3%2F2+-+2i%29+