The equation is x^2 + √(x^2 + 2x + 8) = 12 - 2x.
To solve for x, we need to first isolate the square root term on one side of the equation:
x^2 + √(x^2 + 2x + 8) = 12 - 2x√(x^2 + 2x + 8) = 12 - 2x - x^2√(x^2 + 2x + 8) = 12 - 2x - x^2
Square both sides to eliminate the square root:
x^2 + 2x + 8 = (12 - 2x - x^2)^2x^2 + 2x + 8 = 144 - 48x + 4x^2 - 24x + 4x^3 + 4x^2 + 12x^2
Combine like terms:
x^2 + 2x + 8 = 4x^2 + 12x^2 + 4x^2 - 48x - 24x + 4x^3 + 144x^2 + 2x + 8 = 20x^2 - 72x + 4x^3 + 144
Rearrange the equation to isolate the terms on one side:
4x^3 + 20x^2 - x^2 - 2x + 72x - 144 + 8 = 04x^3 + 19x^2 + 70x - 136 = 0
This is a cubic equation that can be difficult to solve. You may use numerical methods or a graphing calculator to find the approximate solutions for x.
The equation is x^2 + √(x^2 + 2x + 8) = 12 - 2x.
To solve for x, we need to first isolate the square root term on one side of the equation:
x^2 + √(x^2 + 2x + 8) = 12 - 2x
√(x^2 + 2x + 8) = 12 - 2x - x^2
√(x^2 + 2x + 8) = 12 - 2x - x^2
Square both sides to eliminate the square root:
x^2 + 2x + 8 = (12 - 2x - x^2)^2
x^2 + 2x + 8 = 144 - 48x + 4x^2 - 24x + 4x^3 + 4x^2 + 12x^2
Combine like terms:
x^2 + 2x + 8 = 4x^2 + 12x^2 + 4x^2 - 48x - 24x + 4x^3 + 144
x^2 + 2x + 8 = 20x^2 - 72x + 4x^3 + 144
Rearrange the equation to isolate the terms on one side:
4x^3 + 20x^2 - x^2 - 2x + 72x - 144 + 8 = 0
4x^3 + 19x^2 + 70x - 136 = 0
This is a cubic equation that can be difficult to solve. You may use numerical methods or a graphing calculator to find the approximate solutions for x.