## hockeychick23 one year ago What number must be added to each binomial to make a perfect square trinomial? x^2-5x+?

1. LynFran

(-5/2)^2

2. anonymous

$add~\left( half~ the~ co-efficient~ of ~x \right)^2$

3. LynFran

(-5x/2)^2

4. hockeychick23

ok so would it be 25/4 ?

5. anonymous

$$\begin{array}{cccccllllll} {\color{brown}{ a}}^2& + &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\ \downarrow && &&\downarrow \\ {\color{brown}{ a}}&& &&{\color{blue}{ b}}\\ &\to &({\color{brown}{ a}} + {\color{blue}{ b}})^2&\leftarrow \end{array}\qquad % perfect square trinomial, negative middle term \begin{array}{cccccllllll} {\color{brown}{ a}}^2& - &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\ \downarrow && &&\downarrow \\ {\color{brown}{ a}}&& &&{\color{blue}{ b}}\\ &\to &({\color{brown}{ a}} - {\color{blue}{ b}})^2&\leftarrow \end{array}$$ notice, the middle term is 2 * term on left * term on right so the terms without the exponent so 2 * x * "something" = 5x <----- so solve for "something"

6. hockeychick23

oh so its 2*1*x=5 so x= 5/2

7. anonymous

25/4 is correct

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