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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B12x%2B-572+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A9%2A-572=20736.

Discriminant d=20736 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+20736+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+20736+%29%29%2F2%5C9+=+7.33333333333333
x%5B2%5D+=+%28-%2812%29-sqrt%28+20736+%29%29%2F2%5C9+=+-8.66666666666667

Quadratic expression 9x%5E2%2B12x%2B-572 can be factored:
9x%5E2%2B12x%2B-572+=+9%28x-7.33333333333333%29%2A%28x--8.66666666666667%29
Again, the answer is: 7.33333333333333, -8.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B12%2Ax%2B-572+%29