SOLUTION: A square has a perimeter of 100 cm and its area is 9x^2 + 12x + 4 cm^2. What is x?

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Question 495943: A square has a perimeter of 100 cm and its area is 9x^2 + 12x + 4 cm^2. What is x?
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
A square has a perimeter of 100 cm and its area is 9x^2 + 12x + 4 cm^2. What is x?
Since the perimeter is 100 cm
each side is 100/4 = 24 cm
.
area = 24^2
.
24^2 = 9x^2 + 12x + 4
576 = 9x^2 + 12x + 4
0 = 9x^2 + 12x - 572
apply quadratic formula to get:
x = {7.33, -8.67}
we can toss out the negative solution leaving:
x = 7.33
.
details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=20736 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7.33333333333333, -8.66666666666667. Here's your graph:

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