solve c(x)=x^2-40x+405
C(x) = x^2 - 40x + 405 = 0,
Use the Quadratic Formula:
x = ( 40 +- sqrt(400-1620)) / 2,
x = (40 +- sqrt(-20)) / 2,
x = (40 +- sqrt(20*-1)) / 2,
x = (40 +- 4.47i) / 2,
Solution Set:
x = 20 + 2.24i.
x = 20 - 2.24i.
Correction:Replace 400 with 1600.
To solve the quadratic equation c(x) = x^2 - 40x + 405, we can follow a few steps:
Step 1: Set c(x) = 0
x^2 - 40x + 405 = 0
Step 2: Factor the equation, if possible
Since the equation is quadratic, we can try to factor it.
The factors of 405 that add up to -40 are -5 and -45.
Therefore, we can rewrite the equation as:
(x - 5)(x - 45) = 0
Step 3: Set each factor equal to zero and solve for x
x - 5 = 0 or x - 45 = 0
Solving the first equation, we add 5 to both sides:
x = 5
Solving the second equation, we add 45 to both sides:
x = 45
Step 4: Check the solutions
To check if the solutions are valid, substitute them back into the original equation:
For x = 5,
c(5) = 5^2 - 40(5) + 405
= 25 - 200 + 405
= 230
For x = 45,
c(45) = 45^2 - 40(45) + 405
= 2025 - 1800 + 405
= 630
Thus, the solutions of the quadratic equation c(x) = x^2 - 40x + 405 are x = 5 and x = 45.