Question

Solve by completing the square: -7x = 5-x^2

Answer 1

get your "x" terms to the same side:

x^2 -7x +K = 5 +K

we need 2 numbers that are the same that add to get (-7).

Half of -7 + half of -7 are the only thing that fits the bill

so we have (-7/2)

we need to multiply this by itself (square it) to answer what K is.

K = (-7/2)(-7/2) = 49/4

lets plug that in to our equation to get:

x^2 -7x +(49/4) = 5(4)/4 +49/4

The left hand side is a perfect square now.

(x-(7/2))^2 = 69/4 ..lets square both sides to get:

x-(7/2) = +-sqrt(69/4) ..solve for x

x = +-sqrt(69)/2 + (7/2)

I dont know if 69 reduces or not, but you might be able to figure that out :)

Answer 2

completeing the square is just proof that the quadratic formula works.

-(b^2)/2a +-sqrt(b^2 - 4ac)/2a

Answer 3

ack!!! ummm...thats -(b)/2a :)