This is a quadratic equation. To solve it, first let's simplify the equation by combining like terms:
x^2 + 3x - sqrt(x^2 + 3x) - 2 = 0
Next, let's isolate the square root term by moving all other terms to the other side of the equation:
x^2 + 3x - 2 = sqrt(x^2 + 3x)
Now, square both sides of the equation to eliminate the square root:
(x^2 + 3x - 2)^2 = x^2 + 3x
Expanding the left side gives:
(x^2 + 3x - 2)(x^2 + 3x - 2) = x^2 + 3x
x^4 + 3x^3 - 2x^2 + 3x^3 + 9x^2 - 6x - 2x^2 - 6x + 4 = x^2 + 3x
Combine like terms:
x^4 + 6x^3 + 5x^2 - 9x + 4 = x^2 + 3x
Rearrange to set the equation equal to zero:
x^4 + 6x^3 + 4x^2 - 6x + 4 = 0
This is the simplified form of the equation.
This is a quadratic equation. To solve it, first let's simplify the equation by combining like terms:
x^2 + 3x - sqrt(x^2 + 3x) - 2 = 0
Next, let's isolate the square root term by moving all other terms to the other side of the equation:
x^2 + 3x - 2 = sqrt(x^2 + 3x)
Now, square both sides of the equation to eliminate the square root:
(x^2 + 3x - 2)^2 = x^2 + 3x
Expanding the left side gives:
(x^2 + 3x - 2)(x^2 + 3x - 2) = x^2 + 3x
x^4 + 3x^3 - 2x^2 + 3x^3 + 9x^2 - 6x - 2x^2 - 6x + 4 = x^2 + 3x
Combine like terms:
x^4 + 6x^3 + 5x^2 - 9x + 4 = x^2 + 3x
Rearrange to set the equation equal to zero:
x^4 + 6x^3 + 4x^2 - 6x + 4 = 0
This is the simplified form of the equation.