The area of a square garden is represented by the quadratic expression 9x2 - 12x + 4. The length of one side of the square garden is 91 inches. What is the value of x ?
Hint: Since the garden is in the shape of a square, the expression 9x2 - 12x + 4 is the product of two identical factors. Factor the expression to find these identical factors. Each factor represents the length of one side of the square. Therefore, each factor equals 91. Once you make one of the factors equal to 91, you can solve for x.
I personally don't understand this problem at all it gives me a alot of confusion with the 91
since 9 and 4 are both perfect squares, try (3x-2)(3x-2).
To find the value of x, we need to factor the quadratic expression 9x^2 - 12x + 4.
The expression can be factored as (3x - 2)(3x - 2) or (3x - 2)^2.
So, each factor represents the length of one side of the square, and since the garden is in the shape of a square, each factor is equal to 91.
Setting (3x - 2) equal to 91, we can solve for x:
3x - 2 = 91
Adding 2 to both sides:
3x = 93
Dividing both sides by 3:
x = 31
Therefore, the value of x is 31.
To solve this problem, we need to find the value of x given that the length of one side of the square garden is 91 inches.
We are given the quadratic expression 9x^2 - 12x + 4, which represents the area of the square garden. The expression can be factored by looking for two identical factors that multiply to give the quadratic expression. Let's factor it:
9x^2 - 12x + 4 = (3x - 2)(3x - 2)
So, the expression is the product of two identical factors, (3x - 2)(3x - 2).
Now, we know that each factor represents the length of one side of the square. If we set either of the factors equal to 91, we can solve for x. Let's choose one of the factors:
3x - 2 = 91
Now we can solve this equation for x:
3x = 91 + 2
3x = 93
x = 93/3
x = 31
Therefore, the value of x is 31.