Question 221675
Use the quadratic formula to solve the equation for x in terms of y.
{{{ 8x^2-8xy+6(1-y^2)= 0}}} 
:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
In this problems a=8; b=-8y; c=6(1-y^2)
{{{x = (-(-8y) +- sqrt((-8y)^2 - 4 * 8 *6(1-y^2) ))/(2*8) }}}
:
{{{x = (8y +- sqrt(64y^2 - 192(1-y^2) ))/16 }}}
:
{{{x = (8y +- sqrt(64y^2 - 192 + 192y^2) )/16 }}}
:
{{{x = (8y +- sqrt(256y^2 - 192) )/16 }}}; combine like terms
:
{{{x = (8y +- sqrt(64(4y^2 - 3)) )/16 }}}; factor out 64
:
{{{x = (8y +- 8*sqrt(4y^2 - 3) )/16 }}}; extract square root of 64
:
{{{x = (y +- sqrt(4y^2 - 3) )/2 }}}; divide both 8's into 16