x^2= 6x+11

solve the quadratic equation for values of x expressed in simplest radical form

x^2 -6x -11=0

a=1 b=-6 c=-11

I will be happy to critique your work.

how do i solve this ...

-4 (9a-b)+ 3 (5a +2b)

To solve the quadratic equation x^2 = 6x + 11, we can follow these steps:

Step 1: Rewrite the equation in standard form, which means setting one side of the equation equal to zero:
x^2 - 6x - 11 = 0

Step 2: Determine the discriminant (b^2 - 4ac) to determine the nature of the solutions. In this case, the coefficients are:
a = 1, b = -6, and c = -11
The discriminant calculation is:
D = (-6)^2 - 4(1)(-11) = 36 + 44 = 80

Step 3: Since the discriminant (D = 80) is positive, the equation has two distinct real solutions.

Step 4: Apply the quadratic formula to find the solutions:
x = (-b ± √D) / (2a)
Plugging in the values:
x = (-(-6) ± √80) / (2 * 1)
x = (6 ± √80) / 2
x = (6 ± 4√5) / 2

Step 5: Simplify the expression by dividing both the numerator and denominator by 2:
x = 3 ± 2√5

Therefore, the solutions to the quadratic equation x^2 = 6x + 11 are:
x = 3 + 2√5 and x = 3 - 2√5