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Completing the square. SACHS
Contributed by: Shanahan
Step one: move the constant to the other side
x2 + 8x - 9 = 0
x+ 8x       = 
x+ 8x + (
Step two: 'Complete the square'. 
(halve the co-efficient of the x, square it,
add to both sides)
x2 + 8x    = 9
)2 = 9 + (
)2
x2 + 8x +(4)2 = 9 + (4)2
Step three: You have created a 'square' on the left.
Show it and simplify the right.
( x +
)2 = 
Step four: Get the square root of both sides,
then solve for x.
(x + 4)2 = 25
x + 4 = ±√
x = -
x + 4 = ±√25
x =
or x = 
±
     BRING ON
THE FRACTIONS  
Step one: move the constant to the other side
x2 - 5x + 2 = 0
x2 - 5x       = 
x2 - 5x +(-
Step two: 'Complete the square'. 
(halve the co-efficient of the x, square it,
add to both sides)
x2 - 5x    = -2
)2 = -2 +(-
)2
x2 - 5x +(-5)2 = -2 + (-5)2
Step three: You have created a 'square' on the left.
Show it and simplify the right.
(x - 5)2 = -2 +
2
2
2
(x - 5)2 = -2 + 25
(x - 5)2 =
2
2
4
Step four: Get the square root of both sides,
then solve for x.
(x - 5)2 = 17
x - 5 = ±√
2
2
4
x - 5 = ±√17
x - 5±√
2
2
4
x - 5±√17
x =     ±√17
2
2
2
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