Can anyone solve this quadratic by completing the square for me?
Steps you took?
It's been a few years since I've had a problem like this, so hopefully I am going about this correctly. Start by dividing the equation through by 16 to get:
y^2 + y = 1/16
Now, we figure that in order to factor the left hand side of the equation we would need something of the form (y + c)^2 with c denoting some constant value.
We would like to choose something along the lines of:
(y+1/2)^2 because when you multiply it out you get:
y^2 + y + 1/4. But since we have this additional 1/4 on the left side of the equation, we must add it to the right side to get the full equation:
y^2 + y + 1/4 = 1/16 + 1/4
This becomes: (y + 1/2)^2 = (1/4) + (1/16)
which becomes: (y + 1/2)^2 = 5/16.
Now take the square root of both sides to yield:
y + 1/2 = +/- sqrt(5)/4
Final step: subtract 1/2 from both sides to solve for y:
y = (+/- sqrt(5)/4) - 1/2
I hope this explanation is useful.
Edit: This is late, but here it is anyway.
First thing, we have to make the coefficient of the quadratic term 1. So divide all terms by 16.
Now, take half of the coefficient of the linear term, square it, and add it to both sides.
Now, take the square root of both sides.