Question

Hello! I don't know how to start answering questions like this. Please help me :(

Problem: The area of shelly's square shape plant box is x^2+6x+9. What is the length of each side?

Thank you so much!!

Answer 1

If it is a square, the area = s^2 where s is a side length
s^2 = x^2 + 6 x + 9
by sheer luck
x^2 +6 x + 9 = (x+3)( x+3)
so
s = x+3

Answer 2

s² = x² + 6 x + 9 = ( x + 3 )²

s = ± √ ( x + 3 )²

s = ± ( x + 3 )

s must be greater than zero

s = ± ( x + 3 ) > 0

± ( x + 3 ) > 0

You have two solutions:


1.

x + 3 > 0

Subtract 3 to both sides

x > - 3


2.

- ( x + 3 ) > 0

- x - 3 > 0

Add 3 to both sides

- x > 3

Multiply both sides by - 1

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

x < - 3


This means that x can be any real number except - 3

Solution is:

x < - 3 , x > - 3

Or interval notation:

( - ∞ , - 3 ) ∪ ( - 3 , ∞ )