help solve y^2+14=10y

Question

anonymous · Answer

y^2-10y+14=0
use quadratic formula

ay^2+by+c=0
where
a=1
b=-10
c=14

quadratic formula is 
$$\Large y=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

mathstudent55 · Answer

Subtract the 10y term over to the left side, then use the quadratic formula.

whpalmer4 · Answer

Or if you prefer, complete the square:
Put all the terms with powers of y on the left, and numbers on the right
$$y^2-10y = -14$$Now take half the coefficient of the y term, square it, and add to both sides
$$y^2 -10y + (\frac{-10}{2})^2 = -14 + (\frac{-10}{2})^2$$Rewrite the left side as a square
$$(y-5)^2 = 11$$Take square root of both sides$$y-5 = \pm \sqrt{11}$$Solve for y$$y=5\pm\sqrt{11}$$

whpalmer4 · Answer

Important: to complete the square in this manner, you *must* have the coefficient of the squared term = 1.  If it isn't, divide the equation by the coefficient.