Question

x^2-4x-21=0

how do you solve this

Answer 1

x ^ 2 - 4 x - 21 = 0 Add 21 to both sides

x ^ 2 - 4 x - 21 + 21 = 0 + 21

x ^ 2 - 4 x = 21 Add 4 to both sides

x ^ 2 - 4 x + 4 = 21 + 4

x ^ 2 - 4 x + 4 = 25

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Remark :

( a - b ) ^ 2 = a ^ 2 - 2 a b + b ^ 2

That's why :

x ^ 2 - 4 x + 4 = ( x - 2 ) ^ 2

x ^ 2 - 4 x + 4 = 25

( x - 2 ) ^ 2 = 25
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( x - 2 ) ^ 2 = 25

x - 2 = + OR - sqrt ( 25 )

Fist solution :

x - 2 = sqrt ( 25 )

x - 2 = 5 Add 2 to both sides

x - 2 + 2 = 5 + 2

x = 7


Second solution :

x - 2 = - sqrt ( 25 )

x - 2 = - 5 Add 2 to both sides

x - 2 + 2 = - 5 + 2

x = - 3


Solutions are :

x = - 3

and

x = 7

Answer 2

yea that's pretty much it!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111111