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!!
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
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 , ∞ )
Hello! I'd be happy to help you with this question.
To find the length of each side of Shelly's square-shaped plant box, we need to determine the square root of the area. The given area of the plant box is x^2 + 6x + 9.
Step 1: Set up the equation:
The area of a square is equal to the side length squared. In this case, the area (x^2 + 6x + 9) is equal to (side length)^2. So, we have the equation: x^2 + 6x + 9 = (side length)^2.
Step 2: Take the square root:
To find the side length, we need to take the square root of both sides of the equation. Taking the square root will cancel out the squared term on the right side.
√(x^2 + 6x + 9) = √((side length)^2)
Simplifying this equation, we have:
x + 3 = side length
So, the length of each side of Shelly's square-shaped plant box is x + 3.
I hope this explanation helps you understand how to find the length of each side. If you have any additional questions, please feel free to ask!