Step 6: Factor the equation (if possible) or solve using numerical methods. There doesn't seem to be an easy way to factor this polynomial, so we can use numerical methods like the Rational Root Theorem, synthetic division, or graphing to find approximate solutions.
To solve this equation, we need to find the value of x that satisfies the equation.
Step 1: Rewrite the equation in terms of x^2 as the base.
(9 - x^2)^0.5 = - |x^2 + 4x + 3|
√(9 - x^2) = - |x^2 + 4x + 3|
Step 2: Square both sides to eliminate the square root.
9 - x^2 = (x^2 + 4x + 3)^2
Step 3: Expand the right side of the equation.
9 - x^2 = (x^2 + 4x + 3)(x^2 + 4x + 3)
9 - x^2 = x^4 + 8x^3 + 22x^2 + 24x + 9
Step 4: Rearrange the terms and put everything on one side of the equation.
0 = x^4 + 8x^3 + 22x^2 + 24x + 9 - 9 + x^2
Step 5: Simplify the equation.
0 = x^4 + 8x^3 + 23x^2 + 24x
Step 6: Factor the equation (if possible) or solve using numerical methods.
There doesn't seem to be an easy way to factor this polynomial, so we can use numerical methods like the Rational Root Theorem, synthetic division, or graphing to find approximate solutions.