Give the following revenue and cost functions, find the break even point (equilibrium point) R(x)= 56x-2x^2; C(x)=24x+101The X^2 is the only thing that throws me off. Im not sure what im doing.

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neela | High School Teacher | (Level 3) Valedictorian

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The equilibrium point  x= a is the point where,

R(x) = C(x) at x=a or

So,solving for x, when 56x-2x^2=24x+101 or

2x^2+24x-56x+101 = 0, we get a.

2x^2-32x+101 = 0 or

2(x-8)^2-2*8^2+101 =0 or

2(x-8)^2 = 128-101 = 27 or

(x-8)^2 = 27/2 =13.5. or

x=8+sqrt13.5=11.6742 is the break even point where R(11.6742) and C(11.6742) equal and there is no profit and no loss.