For the expressions in questions 1 – 4, choose which number would make the expression a perfect square. Then, choose an equivalent expression in factored form.

1. $x^2+3x$

1. What number can be added to make $x^2+3x$ a perfect square?

2. Which expression is equivalent to $x^2+3x$?

2. $x^2+0.6x$

1. What number can be added to make $x^2+0.6x$ a perfect square?

2. Which expression is equivalent to $x^2+0.6x$?

3. $x^2-11x$

1. What number can be added to make $x^2-11x$ a perfect square?

2. Which expression is equivalent to $x^2-11x$?

4. $x^2-\frac{5}{2}x$

1. What number can be added to make $x^2-\frac{5}{2}x$ a perfect square?

2. Which expression is equivalent to $x^2-\frac{5}{2}x$?

5. What number can be added to make $x^2+x$ a perfect square?

6. What number can be added to make $x^2-\frac{3}{2}x$ a perfect square?  

1. Do you think using the factored form is the best way for Noah to solve this equation?

2. Solve the original equation, then choose the two roots.

1. $x=-4$
2. $x=12$
3. $x=-2$
4. $x=-6$
5. $x=4$

1. $x^2+20x+50=14$. The solutions are $x=-18$ and $x=-2$.

2. $x^2+1.6x=0.36$. The solutions are $x=-1.8$ and $x=0.2$.

3. $x^2-5x=\frac{11}{4}$. The solutions are $x=\frac{11}{4}$ and $x=-12$.

1. $x=-0.5$
2. $x=1$
3. $x=0$
4. $x=2$
5. $x=-1$

2. $x^2+0.8x=0.09$

1. $x=-0.9$
2. $x=0.8$
3. $x=0.4$
4. $x=0.1$
5. $x=0.81$

3. $x^2+\frac{13}{3}x=\frac{56}{36}$

1. $x=\frac{28}{3}$
2. $x=\frac{1}{9}$
3. $x=\frac{112}{36}$
4. $x=-\frac{14}{3}$
5. $x=\frac{1}{3}$