Question

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Complete the square to make a perfect square trinomial. Then, write a result as a binomial squared. m^2-13m

m^2-13+ ? =( ? )^2

Answer 1

Trinomial

`m^2 - 13m + (169)/(4)`

Binomial squared

`(m - (13)/(2))^2`

Explanation:

Given

`m^2-13m`

Required

Make a perfect trinomial

We have:

`m^2-13m =`

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Take the coefficient of m i.e. -13

Divide by 2 i.e. -13/2

Square i.e. (-13/2)

Add to both sides of the equation

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`m^2-13m =` becomes

`m^2 - 13m + ((-13)/(2))^2 = ((-13)/(2))^2`

`m^2 - 13m + (169)/(4) = (169)/(4)`

Expand

`m^2 - (13)/(2)m- (13)/(2)m + (169)/(4) = (169)/(4)`

Factorize:

`m(m - (13)/(2))- (13)/(2)(m - (13)/(2)) = (169)/(4)`

Factor out m - 13/2

`(m - (13)/(2))(m - (13)/(2)) = (169)/(4)`

Write as square

`(m - (13)/(2))^2 = (169)/(4)`

Hence, the trinomial is:

`m^2 - 13m + (169)/(4)`

And the binomial squared is:

`(m - (13)/(2))^2`