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
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!!
2 answers
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 , ∞ )
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 , ∞ )