Question

x^2 +12x - 45 = 0 by method of completing square method

Answer 1

Solving x2-12x+45 = 0 by Completing The Square .

Subtract 45 from both side of the equation :
x2-12x = -45

Now the clever bit: Take the coefficient of x , which is 12 , divide by two, giving 6 , and finally square it giving 36

Add 36 to both sides of the equation :
On the right hand side we have :
-45 + 36 or, (-45/1)+(36/1)
The common denominator of the two fractions is 1 Adding (-45/1)+(36/1) gives -9/1
So adding to both sides we finally get :
x2-12x+36 = -9

Adding 36 has completed the left hand side into a perfect square :
x2-12x+36 =
(x-6) • (x-6) =
(x-6)2
Things which are equal to the same thing are also equal to one another. Since
x2-12x+36 = -9 and
x2-12x+36 = (x-6)2
then, according to the law of transitivity,
(x-6)2 = -9

We'll refer to this Equation as Eq. #2.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of
(x-6)2 is
(x-6)2/2 =
(x-6)1 =
x-6

Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-6 = √ -9

Add 6 to both sides to obtain:
x = 6 + √ -9
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1


Since a square root has two values, one positive and the other negative
x2 - 12x + 45 = 0
has two solutions:
x = 6 + √ 9 • i
or
x = 6 - √ 9 • i




Source: tigeralgebra

Answer 2

hope this help u.........