Question 65430This question is from textbook An Incremental Development
: Solve by completing the square
3x^2 - 4x + 5 = 0
This question is from textbook An Incremental Development
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Solve by completing the square
3x^2 - 4x + 5 = 0
First, divide both sides by 3. (We want the coefficient of x^2 to be 1. This will simplify completing the square). We get:
x^2-(4/3)x+(5/3)=0
Next, subtract (5/3) from both sides. This removes the "C" term from the left side. We will now choose another "C" term that will result in a perfect square on the left side and then we will add it to both sides:
x^2-(4/3)x=-(5/3)
Now, we will complete the square. Take half of the "x" coefficient (1/2)(4/3), square it ((1/2)(4/3))^2 and add it to both sides:
((1/2)(4/3))^2=(4/6)^2=16/36 so we add 16/36 to both sides:
x^2-(4/3)x+(16/36)=-(5/3)+(16/36)
Let's simplify the right side of the equation
-(5/3)+(16/36)=-(60/36)+(16/36)=-44/36
Note: the left side is a perfect square:
(x-4/6)^2=-44/36
Take sqrt of both sides:
x-4/6=+or-sqrt(-44/36) add 4/6 to both sides:
x=(4/6)+or-((i)sqrt(44))/6 simplifying:
x=(4+or-((i)sqrt(4)(11)))6 and this equals
x=(4+or-(2i)sqrt(11))/6 or
x=(2+(i)sqrt(11))/2
x=(2-(i)sqrt(11))/2
Happy holidays----ptaylor
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