Question

x²-x-90=0 by completing square
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Answer 1

Answer:

hey mate!!

Step-by-step explanation:

hope it will help you !!

thanks!!

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Add  90  to both side of the equation :  

  x2-x = 90

Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4  

Add  1/4  to both sides of the equation :

 On the right hand side we have :

  90  +  1/4    or,  (90/1)+(1/4)  

 The common denominator of the two fractions is  4   Adding  (360/4)+(1/4)  gives  361/4  

 So adding to both sides we finally get :

  x2-x+(1/4) = 361/4

Adding  1/4  has completed the left hand side into a perfect square :

  x2-x+(1/4)  =

  (x-(1/2)) • (x-(1/2))  =

 (x-(1/2))2  

Things which are equal to the same thing are also equal to one another. Since

  x2-x+(1/4) = 361/4 and

  x2-x+(1/4) = (x-(1/2))2  

then, according to the law of transitivity,

  (x-(1/2))2 = 361/4

We'll refer to this Equation as  Eq. #3.2.1  

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

Note that the square root of

  (x-(1/2))2   is

  (x-(1/2))2/2 =

 (x-(1/2))1 =

  x-(1/2)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(1/2) = √ 361/4  

Add  1/2  to both sides to obtain:

  x = 1/2 + √ 361/4  

Since a square root has two values, one positive and the other negative

  x2 - x - 90 = 0

  has two solutions:

 x = 1/2 + √ 361/4  

  or

 x = 1/2 - √ 361/4  

Note that  √ 361/4 can be written as

 √ 361  / √ 4   which is 19 / 2

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Answer 2

Step-by-step explanation:

we can solve it by the formula

=(-b +- √b^2-4ac)/2a

Two roots will be

{ 1 +√1-(-360)}/2 and {1-√1-(-360)}/2

(1+√361)/2 and (1-√361)/2