Completing the square: x^2 + 4x = 9

for completing the square

x^2 + 4x = 9

halve the coefficient of the linear term (that's the "4"), and square the result, then add the result to to both sides ... (half of 4 is 2, 2^2 = 4)

x^2 + 4x + 4 = 9 + 4

x^2 + 4x + 4 = 13

the left side is a perfect square ... factor it

(x + 2)^2 = 13

"un"square both sides ...

x + 2 = +/- sqrt(13)

isolate x ...

x = -2 +/- sqrt(13)

you're done, kapish?
 
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