anonymous
  • anonymous
Solve by completing the square: -7x = 5-x^2
Mathematics
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
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 :)
amistre64
  • amistre64
completeing the square is just proof that the quadratic formula works. -(b^2)/2a +-sqrt(b^2 - 4ac)/2a
amistre64
  • amistre64
ack!!! ummm...thats -(b)/2a :)

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