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