√(x+2)+√(2x-1)=-2
√(x^2-9)=3x-11

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To solve the first equation, we can start by isolating one of the radicals:

√(x+2) = -√(2x-1) - 2

Square both sides to get rid of the square root:

(x+2) = (2x-1) + 4√(2x-1) + 4

Rearrange the terms:

2√(2x-1) = x - 3

Square both sides again:

4(2x-1) = x^2 - 6x + 9

Expand and simplify:

8x - 4 = x^2 - 6x + 9

Rearrange the terms to form a quadratic equation:

x^2 - 14x + 13 = 0

Now we can solve this quadratic equation to find the possible values of x. Factoring or using the quadratic formula gives us:

x = 1 or x = 13

We can substitute these values back into the original equation to confirm if they satisfy the equation.

For the second equation:

√(x^2-9) = 3x-11

Square both sides to get rid of the square root:

x^2 - 9 = (3x-11)^2
x^2 - 9 = 9x^2 - 66x + 121

Rearrange the terms:

8x^2 - 66x + 130 = 0

This is also a quadratic equation that can be solved using factoring or the quadratic formula. We get:

x = 2 or x = 8

We can substitute these values back into the original equation to confirm if they satisfy the equation.