Solve for x in the equation x^2+10x+12=36

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Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-

tester [12383]

To achieve a positive profit p(x)>0, we start with:
$-100 x^{2} +350x-150 \ \textgreater \ 0$

Next, we solve for x:
$-2 x^{2} +7x-3 \ \textgreater \ 0$

The parameters are:
a = -2
b = 7
c = -3

We will apply the quadratic formula:
$x_{1} = \frac{-b+ \sqrt{ b^{2}-4ac } }{2a} \\ \\ x_{2} = \frac{-b- \sqrt{ b^{2}-4ac } }{2a} \\ \\ x_{1} = \frac{-7+ \sqrt{ 49-24 } }{-4} = \frac{-7+5 }{-4} = \frac{-2 }{-4} = \frac{1}{2} \\ \\ x_{2} = \frac{-7- \sqrt{ 49-24 } }{-4} = \frac{-7-5 }{-4} = \frac{-12 }{-4} = 3$

This yields two results—one a fraction, the other a whole number. We focus on the whole number since the muffins sold must be a complete unit. Thus we conclude:
x>3

5 0

3 months ago

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What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

lawyer [12517]

Answer:

$x=-2.38$