5.3.5 Journal:Completing the Square

Malcolm wants to build an outdoor stage with a total area of 350 square feet. The length of the stage should be three feet shorter than the width. He calculated the equation to bew² 3w= 350

2. Malcolm and his bandmate have different ideas for figuring out the equation. Which one do you think will make it easiest to solve the equation? Why? (2 points)

3. To make a perfect square trinomial, Malcolm said the rule for figuring out the number to add is. Is he correct? If not, what is the rule? (1 point)

4. Calculate the number that you need to add to each side of the equationw² 3w= 350to perfect square trinomial. Show your work. (3 points)

5. Factor the trinomial. (3 points)

6. Now that you've factored the equation, find the square root of each side and solve forw. Show your work. (2 points)

7. What are the maximum dimensions of the stage that Malcolm can build? (Round to the nearest foot.) (2 points)

w= _____

l= _____

8. There's been a last-minute change of plans. The lumberyard has decided to donate 480 square feet of lumber, and Malcolm's band now wants the length of the stage to be four feet shorter than the width. equation that reflects the new requirements. (2 points)

9. Using the new equation, complete the square and solve forw. (2 points)

10. What are the new dimensions of the stage? (1 point)