Find the value of c that completes the square x^2+(7/13)x+c

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the expression x^2+(7/13)x+c and we need to find c to complete the square.

Now if we have (x + a)^2 = x^2 + 2ax + a^2

Here 2a = 7/13

=> a = (7/13) / 2

=> a = 7/26

a^2 = c = (7/26)^2

=> 49/676

Therefore c= 49/676.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let f(x) = x^2 + (7/13) x + c .

Given that f(x) is a complete square.

We need to find the values if C.

==> f(x) = ( x+ (7/13)/2) ^2 = x^2 + 7/13 x + C

   Let us open the the brackets.

==> ( x+ 7/26)^2 = x^2 + 7/13x  C

==> x^2 + (7/13) x + (7/26)^2  = x^2 + 7/13 x + c

Then we conclude that C = (7/26)^2

==> C = 49/ 676

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To find the value of c that completes the square x^2+(7/13)x+c.

(x+a)^2 = x^2+2ax+a^2 is an identity.

We now conder   x^2+(7/13)x+ c = x^2+2ax+a^2 is an identity.

Since the leading terms are equal, we  equate x terms:

2ax = (7/13)x.

So a = (7/13)/2

=> a = 7/26

Now we equate constant terms:

c = a^2 = (7/26)^2 = 49/676.

Therefore c = 49/676 which makes x^2+(7/13)x+c a perfect square.

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The formula (a+b)^2 = a^2 + 2ab + b^2 will guide us.

We'll put a^2 = x^2 => a = x

2xb = x*(7/13)

We'll divide by x:

2b = 7/13

We'll divide by 2:

b = 7/13*2

b = 7/26

We'll raise to square:

b^2 = (7/26)^2

b^2 = 49/676

The missing term that completes the square is c = 49/676.

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