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Charlotte-Mecklenburg Schools (CMS) is going to host a Superhero "Dinner and a Movie" fundraiser at a local theater. Tickets will be for dinner and a screening of Wakanda Forever. They hire you as a consultant to help set the selling price of the tickets. You analyze the costs and consumer demands and arrive at a function for the profit, P(x)=-x^(2)+90 x-100, where x represents the price of a ticket for dinner and watching Wakanda Forever. What are the break-even points (the selling prices for which the profit is $0 )? Give answers to the nearest cent. {:[x=$◻" (left-most break-even point) "],[x=$◻" (right-most break-even point "]:} (right-most break-even point)

Charlotte-Mecklenburg Schools (CMS) is going to host a Superhero ＂Dinner and a Movie＂ fundraiser at a local theater. Tickets will be for dinner and a screening of Wakanda Forever. They hire you as a consultant to help set the selling price of the tickets. You analyze the costs and consumer demands and arrive at a function for the profit, P(x)=−x2+90x−100P(x)=-x^{2}+90x-100, where xx represents the price of a ticket for dinner and watching Wakanda Forever.\newlineWhat are the break-even points (the selling prices for which the profit is \newline$0\$0 )? Give answers to the nearest cent.\newlinex=x= $\$◻(left-most break-even point)\newlinex=x= $\$◻(right-most break-even point)

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Q. Charlotte-Mecklenburg Schools (CMS) is going to host a Superhero ＂Dinner and a Movie＂ fundraiser at a local theater. Tickets will be for dinner and a screening of Wakanda Forever. They hire you as a consultant to help set the selling price of the tickets. You analyze the costs and consumer demands and arrive at a function for the profit, P(x)=−x2+90x−100P(x)=-x^{2}+90x-100, where xx represents the price of a ticket for dinner and watching Wakanda Forever.\newlineWhat are the break-even points (the selling prices for which the profit is \newline$0\$0 )? Give answers to the nearest cent.\newlinex=x= $\$◻(left-most break-even point)\newlinex=x= $\$◻(right-most break-even point)
  1. Identify profit function: Identify the profit function and set it to zero to find the break-even points.\newlineP(x)=−x2+90x−100P(x) = -x^2 + 90x - 100\newlineSet P(x)=0P(x) = 0 to find the values of xx.\newline0=−x2+90x−1000 = -x^2 + 90x - 100
  2. Solve quadratic equation: Solve the quadratic equation using the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, a=−1a = -1, b=90b = 90, and c=−100c = -100. x=−90±(90)2−4(−1)(−100)2(−1)x = \frac{-90 \pm \sqrt{(90)^2 - 4(-1)(-100)}}{2(-1)} x=−90±8100−400−2x = \frac{-90 \pm \sqrt{8100 - 400}}{-2}
  3. Continue calculation: Continue the calculation from Step 22.\newlinex=−90±7700−2x = \frac{{-90 \pm \sqrt{7700}}}{{-2}}\newlinex=−90±87.74−2x = \frac{{-90 \pm 87.74}}{{-2}}\newlinex=−90+87.74−2x = \frac{{-90 + 87.74}}{{-2}} and x=−90−87.74−2x = \frac{{-90 - 87.74}}{{-2}}
  4. Calculate specific values: Calculate the specific values for xx.x1=(−90+87.74)−2=−1.13x_1 = \frac{{(-90 + 87.74)}}{{-2}} = -1.13x2=(−90−87.74)−2=88.87x_2 = \frac{{(-90 - 87.74)}}{{-2}} = 88.87

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