Question 238836
Problem:x^2 -8x + 30 = 0
My work:a=1, b=-8, c=30
:
{{{x = (-(-8) +- sqrt(-8^2-4*1*30 ))/(2*1) }}}
:
{{{x = (8 +- sqrt(64 - 120 ))/2 }}}
:
{{{x = (8 +- sqrt(-56 ))/2 }}}
:
{{{x = (8 +- sqrt(-4*14))/2 }}}
:
{{{x = (8 +- 2i*sqrt(14))/2 }}}
:
{{{x = 4 +- i*sqrt(14) }}}; I got the same thing you got
:
Hey!
We can prove it, find the equation using our solution:
{{{x = 4 +- i*sqrt(14) }}}
:
{{{x - 4 = i*sqrt(14) }}}
:
Square both sides
(x-4)^2 = i^2(14)
Which is
x^2 - 8x + 16 = -1(14)
x^2 - 8x + 16 = -14
x^2 - 8x + 16 + 14 = 0
x^2 - 8x + 30 = 0; does that look familiar?