SOLUTION: Solve by completing the square : 7 = 3x - 2x^2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve by completing the square : 7 = 3x - 2x^2       Log On


   

Question 65590This question is from textbook An Incremental Development
: Solve by completing the square :
7 = 3x - 2x^2
This question is from textbook An Incremental Development

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2%2F-2%2B3x%2F-2=7%2F-2
x%5E2-%283%2F2%29x=-7%2F2
Multiply the coefficient of x, -(3/2) by 1/2, square it and add it to both sides of the equation. %28%281%2F2%29%2A%28-3%2F2%29%29%5E2=%28-3%2F4%29%5E2=9/16
x%5E2-%283%2F2%29x%2B9%2F16=-7%2F2%2B9%2F16
%28x-3%2F4%29%5E2=-7%2A8%2F%282%2A8%29%2B9%2F16
%28x-3%2F4%29%5E2=-56%2F16%2B9%2F16
%28x-3%2F4%29%5E2=-47%2F16
sqrt%28%28x-3%2F4%29%5E2%29=%2B-sqrt%28-47%2F16%29<--if you haven't had complex numbers yet, you can stop here and say "no real solution," if you have, keep going:
x-3%2F4=%2B-sqrt%2847%29i%2F4
x-3%2F4%2B3%2F4=3%2F4%2B-sqrt%2847%29i%2F4
x=%283%2B-sqrt%2847%29i%29%2F4
Happy Calculating!!!