Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day0.3x^2+12x+14=0
To determine the projected ticket sales for each day, we need to solve the quadratic equation 0.3x^2 + 12x + 14 = 0.
The quadratic equation is in the form of ax^2 + bx + c = 0, where a, b, and c are coefficients. In this case, a = 0.3, b = 12, and c = 14.
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we get:
x = (-(12) ± √((12)^2 - 4(0.3)(14))) / (2(0.3))
Simplifying further:
x = (-12 ± √(144 - 16.8)) / 0.6
x = (-12 ± √(127.2)) / 0.6
Now we have two possible solutions for x:
x1 = (-12 + √(127.2)) / 0.6
x2 = (-12 - √(127.2)) / 0.6
Calculating these values will give us the approximate number of days until the tickets sell out, based on the projected ticket sales.