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2 Comments Already

mygif
1999 Nissan Skyline GTR Vspec Said,
February 5th, 2011 @4:48 pm  

there is a theorem??

mygif
Pi R Squared Said,
February 5th, 2011 @5:28 pm  

Hi,

Given the quadratic formula ax² + bx + c = 0, solve it by completing the square.

ax² + bx + c = 0
Move constant to the other side.

ax² + bx = -c
Divide every term by “a”.

x² + (b/a)x = -c/a
Complete the square on the left side. Multiply ½ times the x coefficient. Square the result and add that amount to both sides.

x² + (b/a)x = -c/a
½(b/a) = b/(2a) [b/(2a)]² = b²/(4a²)

x² + (b/a)x + b²/(4a²) = -c/a + b²/(4a²)
Factor the left side. Re-arrange the right side.

(x + b/(2a))² = b²/(4a²) – c/a
Re-write the right side with a common denominator of 4a².

(x + b/(2a))² = b²/(4a²) – 4ac/(4a²)

(x + b/(2a))² = (b² – 4ac)/(4a²)
Take the square root of both sides. Put a ± in front of the radical on the right side.
……. ……. …… _______
x + b/(2a) = ± ?(b² – 4ac)/(2a)
Get x alone.
……. ……. …. _______
x = -b/(2a) ± ?(b² – 4ac)/(2a)

… …. ._______
-b ± ?(b² – 4ac)
———————– = x
…….2a

This is the quadratic formula, so it can be derived from completing the square on a quadratic equation. I hope that helps!! :-)

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