Question

solve the given equation by method of completing the squares
$x{ {}^{2} } ^ +12x - 45 = 0$
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Answer 1

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x^2 + 12 x - 45 = 0

=> x^2 + 12x =45

add (6)^2 both side

=> x^2 + 12x + (6)^2 = 45 + (6)^2 

=> x^2 + 2. (6).x + (6)^2 = 81 =(9)^2 

=>(x + 6)^2 = (9)^2 

=> (x + 6)^2 -(9)^2 = 0
use formula, 
a^2 - b^2 = (a - b)(a + b)

now,
=>(x + 6 -9)(x + 6 + 9)=0

=> x=3 , -15 , hence roots of equation is 3 and -15




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Answer 2

hi

X²+12x-45=0

So by method of completing square,

we have the form of (x+a)2=x²+2ax+c

So x²+2(6)x-45=0

Here the value of a = 6

So, a²= 36

So, adding and subtracting 36,

we get,

x²+2(6)x+36-36-45=0

⇒(x+6)²-81=0

⇒(x+6)²-9²=0

⇒(x+6)²=9²

⇒(x+6) = ±9

⇒x=-6±9

⇒x=3,-15

hope this helps you