(x%5E2-2x%2B4)-x(x%5E2-5)%3D15.jpeg "(x+2)(x^2-2x+4)-x(x^2-5)=15")
Solving the Equation (x+2)(x^2-2x+4)-x(x^2-5)=15
This article will guide you through the steps of solving the given equation: (x+2)(x^2-2x+4)-x(x^2-5)=15.
1. Expanding the Equation
First, we need to expand the equation by multiplying the terms:
- (x+2)(x^2-2x+4): This is a special product called the sum of cubes. It can be expanded directly as: x^3 + 2^3 = x^3 + 8
- x(x^2-5): This simplifies to x^3 - 5x
Now our equation looks like this: x^3 + 8 - x^3 + 5x = 15
2. Simplifying the Equation
Combining like terms, we get: 5x + 8 = 15
3. Isolate the Variable
To isolate the variable 'x', we need to subtract 8 from both sides: 5x = 7
4. Solving for 'x'
Finally, divide both sides by 5 to get the value of x: x = 7/5
Therefore, the solution to the equation (x+2)(x^2-2x+4)-x(x^2-5)=15 is x = 7/5.