SOLUTION: find all solutions of the equation 2x^2 - 8x + 16 = 0 and express them in the form a + bi

Algebra ->  Equations -> SOLUTION: find all solutions of the equation 2x^2 - 8x + 16 = 0 and express them in the form a + bi      Log On


   

Question 519839: find all solutions of the equation 2x^2 - 8x + 16 = 0 and express them in the form a + bi
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-8x%2B16=0 Start with the given equation.


Notice that the quadratic 2x%5E2-8x%2B16 is in the form of Ax%5E2%2BBx%2BC where A=2, B=-8, and C=16


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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%282%29%2816%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-8, and C=16


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%282%29%2816%29+%29%29%2F%282%282%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%282%29%2816%29+%29%29%2F%282%282%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-128+%29%29%2F%282%282%29%29 Multiply 4%282%29%2816%29 to get 128


x+=+%288+%2B-+sqrt%28+-64+%29%29%2F%282%282%29%29 Subtract 128 from 64 to get -64


x+=+%288+%2B-+sqrt%28+-64+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%288+%2B-+8%2Ai%29%2F%284%29 Take the square root of -64 to get 8%2Ai.


x+=+%288+%2B+8%2Ai%29%2F%284%29 or x+=+%288+-+8%2Ai%29%2F%284%29 Break up the expression.


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


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


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

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim