Question

Part of the roof of a factory is devoted to mechanical support and part to green space. The area G that is designated as green space can be modeled by the polynomial 2x2 - 7x and the area M that is devoted to mechanical support can be modeled by the polynomial x2 - 9x + 24. Given that the area R of the roof is 36 square yards, write and solve a quadratic equation to find the total area of the green space. **Use the positive value for your solution.
(Hint: R = G + M)

Answer 1

Answer:

$36 = 2x^2 -7x +x^2 -9x +24$

$12= 3x^2 -16 x$

And we can rewrite this expression like this:

$3x^2 -16 x -12 =0$

And we can use the quadratic formual to solve this problem:

$X =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}$

With a = 3, b = -16 , c =-12. Replacing we got:

$x = \frac{16 \pm \sqrt{(-16)^2 -4*(3)*(-12)}}{2*3}$

And the solutions for this case are:

$x_1 = 6, x_2 =-\frac{2}{3}$

And then since we need to select the positive solution the final answer would be:

$x = 6$

Step-by-step explanation:

For this case we have the following equations for the total area of the green space:

$G = 2x^2 -7x$

$M = x^2 -9x +24$

And the total area is given by 36 yd^2. And we know that:

$R = 36 yd^2 = G+M$

Replacing the info given we got:

$36 = 2x^2 -7x +x^2 -9x +24$

$12= 3x^2 -16 x$

And we can rewrite this expression like this:

$3x^2 -16 x -12 =0$

And we can use the quadratic formual to solve this problem:

$X =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}$

With a = 3, b = -16 , c =-12. Replacing we got:

$x = \frac{16 \pm \sqrt{(-16)^2 -4*(3)*(-12)}}{2*3}$

And the solutions for this case are:

$x_1 = 6, x_2 =-\frac{2}{3}$

And then since we need to select the positive solution the final answer would be:

$x = 6$