How do you solve by completing the square for $x^2 - 5x = 9$ ?

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Answer 1 · 2015-06-14T20:06:39

$(x-5/2)^2 = x^2-5x+25/4 = 9+25/4 = 61/4$

Hence: $x = 5/2+-sqrt(61)/2$

$(x-5/2)^2$

$= x^2-5x+25/4$

$= 9+25/4$

$= 36/4+25/4$

$= (36+25)/4$

$= 61/4$

So:

$x - 5/2 = +-sqrt(61/4) = +-sqrt(61)/sqrt(4) = +-sqrt(61)/2$

Add $5/2$ to both ends to get:

$x = 5/2+-sqrt(61)/2$

In general,

$ax^2+bx+c = a(x+b/(2a))^2 + (c - b^2/(4a))$

How do you solve by completing the square for x^2 - 5x = 9x^2 - 5x = 9?