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Question 65134: Solve by completing the square. Show your steps: 2x^2 - 3x + 5 = 0
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Solve by completing the square. Show your steps:
2x^2 - 3x + 5 = 0 First we'll divide both sides by 2. Why? Because in the standard form of the quadratic equation (Ax^2+Bx+C=0). I find the problem easier if A is 1. Also, if the quadratic is factorable and A is 1 then B is the sum of the products of C.
Dividing by 2 we get:
x^2-(3/2)x+5/2=0 subtract 5/2 from both sides:
x^2-(3/2)x=-5/2 If we take 1/2 of the B term (1/2)(3/2),
square it ((1/2)(3/2))^2 and add it to both sides, the left side will be a perfect square.
((1/2)(3/2))^2=(3/4)^2=9/16. Now we'll add this to both sides and we have:
x^2-(3/2)x+9/16=-5/2+9/16 =-40/16+9/16 simplifying
x^2-(3/2)x+9/16=-31/16 Factoring the left side we get:
(x-3/4)^2=-31/16 Take sqrt of both sides:
x-3/4=+or-sqrt(-31/16) =+or-((i)sqrt(31)/4 Now add 3/4 to both sides:
x=3/4+or-((i)sqrt(31))/4 so we have:
x=(3+(i)sqrt(31))/4
x=(3-(i)sqrt(31))/4
Hope this helps some. Happy holidays-----ptaylor
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