When the solution of x2 − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r?

x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a

6
42
57
105

1 answer

The equation x^2 - 9x - 6 can be written as x^2 - 9x - 6 = 0.

By comparing it to the general quadratic equation form ax^2 + bx + c = 0, we have a = 1, b = -9, and c = -6.

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a:

x = (9 ± √((-9)^2 - 4*1*(-6))) / 2*1
x = (9 ± √(81 + 24)) / 2
x = (9 ± √105) / 2

Therefore, the value of r is 105.