use the quadratic equation x^2-22x=75 to answer the following questions
Part C - solve the quadratic equation to find the positive solution for x
To solve the quadratic equation x^2 - 22x = 75 to find the positive solution for x, we need to rearrange the equation in the standard quadratic form (ax^2 + bx + c = 0).
So, let's rearrange the equation:
x^2 - 22x - 75 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -22, and c = -75.
Substituting the values in the quadratic formula, we get:
x = (-(-22) ± √((-22)^2 - 4(1)(-75))) / (2*1)
x = (22 ± √(484 + 300)) / 2
x = (22 ± √(784)) / 2
x = (22 ± 28) / 2
So, there are two possible solutions for x:
1. x = (22 + 28) / 2 = 50 / 2 = 25
2. x = (22 - 28) / 2 = -6 / 2 = -3
However, we are looking for the positive solution for x, so the positive solution is x = 25.