Question

Solve for x in the equation
`2x^2-5x+1=3` by completing the square.

Answer 1

2x^2 - 5x - 4 = 0

Next, divide all terms by 2 to make the coefficient of x^2 equal to one:

x^2 - (5/2)x - 2 = 0

The next step in completing the square involves adding and subtracting (b/2)^2 inside the parentheses. The b here refers to the coefficient of x, which is -(5/2). Therefore, (b/2)^2 is ((-5/4))^2 = 6.25.

Here's how it looks when we add and subtract this value:

x^2 - (5/2)x + (5/4)^2 - (5/4)^2 - 2 = 0
(x-(5/4))^2 - (5/4)^2 - 8 = 0
(x-(5/4))^2 = (5/4)^2 + 8

Now take the square root of both sides:

x-(5/4) = ± sqrt((25/16)+32)
x= (5±sqrt(537))/4

So, there are two solutions for x:

x= [(5+sqrt(537)) /8] and x= [(5-sqrt(537)) /8]