The area of a square garden is represented by the quadratic expression 9x^2 - 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 9x^2 - 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 got (3x-2)(3x-2) but now i don't know what to after that so i can get the answer please.
sure you do. Did you not read where it said
Therefore, each factor equals 91?
3x-2 = 91
3x = 93
x = 31
It's hard to solve a problem if you don't read it!
3x-2 = 91
Solve for x.
Great job on factoring the quadratic expression correctly! Now that you have (3x-2)(3x-2), you can set one of the factors equal to 91 and solve for x.
Let's set 3x-2 equal to 91:
3x - 2 = 91
Now, let's solve for x:
Add 2 to both sides:
3x = 93
Divide both sides by 3:
x = 31
Therefore, the value of x is 31.
Great job factoring the expression! You correctly factored the quadratic expression as (3x-2)(3x-2). Now, since each factor represents the length of one side of the square garden, we can set them equal to 91 inches and solve for x.
(3x-2)(3x-2) = 91
To solve this equation, we can use the method of setting each factor equal to the square root of 91.
First, let's set 3x-2 equal to the positive square root of 91:
3x-2 = √91
Next, let's solve for x by isolating x on one side of the equation:
3x = 2 + √91
Dividing both sides by 3:
x = (2 + √91) / 3
So the value of x is (2 + √91) / 3, which is approximately 6.27.
Therefore, the value of x is approximately 6.27 inches.