Question 1084659: Please help me solve this problem, and fill in the blanks?
Michael builds a rectangular deck with an area of 50 square feet. The area is represented by the expression given below.
x^2+5x
Find the width of the deck, and complete the given statements.
Step 1: x^2+5x=50
Step 2: x(x+5)=50 The length is x. What is the width? ___
Step 3: x^+5x-50=0
Step 4: (x+10)(x-5)=0
Because the length can't be ___, the length is 5, and the width is ___.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the area of the deck is 50 square feet.
the area is represented by x^2 + 5x
your equation becomes x^2 + 5x = 50
subtract 50 from both sides of this equation to get x^2 + 5x - 50 = 0
factor this quadratic equation to get (x+10) * (x-5) = 0
your questions are:
Step 1: x^2+5x=50
correct.
Step 2: x(x+5)=50 The length is x. What is the width? ___
if the length is x, then the width has to be x + 5.
Step 3: x^2 + 5x - 50 = 0
correct.
Step 4: (x+10)(x-5)=0
correct.
Because the length can't be ___, the length is 5, and the width is ___.
your factors are (x+10) * (x-5) = 0
to make this equation true, either x+10 is equal to 0 or (x-5) is equal to 0, or both.
set each factor equal to 0 and solve for x.
with x + 10 = 0, solve for x to get x = -10
with x - 5 = 0, solve for x to get x = 5
the length of the rectangle has to be positive, so x can't be equal to -10, therefore x = 5.
x is equal to 5 which represents the length.
x+5 is equal to 10 which represents the width.
length * width = 5 * 10 which is equal to 50 square feet.
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