Question 65590
Solve by completing the square :

7 = 3x - 2x^2

Let's change the order, so it looks more like the other problems you've probably been doing:
-2x^2+3x=7
Divide everything by the coefficient of x^2, -2
{{{-2x^2/-2+3x/-2=7/-2}}}
{{{x^2-(3/2)x=-7/2}}}
Multiply the coefficient of x, -(3/2) by 1/2, square it and add it to both sides of the equation. {{{((1/2)*(-3/2))^2=(-3/4)^2}}}=9/16
{{{x^2-(3/2)x+9/16=-7/2+9/16}}}
{{{(x-3/4)^2=-7*8/(2*8)+9/16}}}
{{{(x-3/4)^2=-56/16+9/16}}}
{{{(x-3/4)^2=-47/16}}}
{{{sqrt((x-3/4)^2)=+-sqrt(-47/16)}}}<--if you haven't had complex numbers yet, you can stop here and say "no real solution," if you have, keep going:
{{{x-3/4=+-sqrt(47)i/4}}}
{{{x-3/4+3/4=3/4+-sqrt(47)i/4}}}
{{{x=(3+-sqrt(47)i)/4}}}
Happy Calculating!!!