What is the number of real solutions?

–11x2 = x + 11

1 answer

To find the number of real solutions for the equation -11x^2 = x + 11, we need to solve for x.

First, let's rearrange the equation to bring all the terms to one side:

-11x^2 - x - 11 = 0

To solve this quadratic equation, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -11, b = -1, and c = -11.

Plugging in the values into the quadratic formula:

x = (-(-1) ± √((-1)^2 - 4(-11)(-11))) / (2(-11))
x = (1 ± √(1 - 484)) / (-22)
x = (1 ± √(-483)) / (-22)

Since the discriminant (b^2 - 4ac) is negative (√(-483)), the quadratic equation has no real solutions.

Therefore, the number of real solutions for -11x^2 = x + 11 is 0.