SOLUTION: Hello! I'm having trouble getting the correct answer for this problem with the quadratic formula. Find all solutions of the equation and express them in the form a + bi. 4x^2-

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello! I'm having trouble getting the correct answer for this problem with the quadratic formula. Find all solutions of the equation and express them in the form a + bi. 4x^2-      Log On


   

Question 196505: Hello!
I'm having trouble getting the correct answer for this problem with the quadratic formula.
Find all solutions of the equation and express them in the form a + bi.
4x^2-8x+7=0
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-8x%2B7=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=-8, and c=7


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%284%29%287%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-8, and c=7


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%284%29%287%29+%29%29%2F%282%284%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%284%29%287%29+%29%29%2F%282%284%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-112+%29%29%2F%282%284%29%29 Multiply 4%284%29%287%29 to get 112


x+=+%288+%2B-+sqrt%28+-48+%29%29%2F%282%284%29%29 Subtract 112 from 64 to get -48


x+=+%288+%2B-+sqrt%28+-48+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%288+%2B-+4i%2Asqrt%283%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%288%2B4i%2Asqrt%283%29%29%2F%288%29 or x+=+%288-4i%2Asqrt%283%29%29%2F%288%29 Break up the expression.


x+=+8%2F8%2B%284i%2Asqrt%283%29%29%2F%288%29 or x+=+8%2F8-%284i%2Asqrt%283%29%29%2F%288%29 Break up the fraction


x+=+1%2B%28i%2Asqrt%283%29%29%2F%282%29 or x+=+1-%28i%2Asqrt%283%29%29%2F%282%29 Reduce



x+=+1%2B%28sqrt%283%29%2F2%29%2Ai or x+=+1-%28sqrt%283%29%2F2%29%2Ai Rearrange the terms.


So the answers are x+=+1%2B%28sqrt%283%29%2F2%29%2Ai or x+=+1-%28sqrt%283%29%2F2%29%2Ai


which are in a%2Bbi form where a=1 and b=sqrt%283%29%2F2