(x%5E2%2B2x%2B7)%2B2(x%5E2-4)-5(x-2)%3D0.jpeg "(x-2)(x^2+2x+7)+2(x^2-4)-5(x-2)=0")
Solving the Equation (x-2)(x^2+2x+7)+2(x^2-4)-5(x-2)=0
In this article, we will solve the equation (x-2)(x^2+2x+7)+2(x^2-4)-5(x-2)=0.
Step 1: Expand the Equation
Let's start by expanding the equation:
(x-2)(x^2+2x+7) = x^3 + 2x^2 + 7x - 2x^2 - 4x - 14 = x^3 - 2x - 14
Now, let's expand the second part of the equation:
2(x^2-4) = 2x^2 - 8
And the third part:
-5(x-2) = -5x + 10
Step 2: Combine the Expanded Equations
Now, let's combine the expanded equations:
x^3 - 2x - 14 + 2x^2 - 8 - 5x + 10 = 0
Step 3: Simplify the Equation
Let's simplify the equation by combining like terms:
x^3 + 2x^2 - 7x - 12 = 0
Conclusion
The final equation is x^3 + 2x^2 - 7x - 12 = 0. This equation is a cubic equation, which can be solved using various methods, such as factoring, the rational root theorem, or numerical methods.
Note that the solution to this equation may not be straightforward, and may require advanced mathematical techniques or numerical methods to solve.
