(x%5E2%2B2x%2B4)-x%5E2(x%2B3)%2B8%3D0.jpeg "(x+1)(x^2+2x+4)-x^2(x+3)+8=0")
Solving the Equation: (x+1)(x^2+2x+4)-x^2(x+3)+8=0
This article will guide you through the steps to solve the given equation:
(x+1)(x^2+2x+4)-x^2(x+3)+8=0
Step 1: Expand the equation
First, we need to expand the equation by multiplying the terms:
- (x+1)(x^2+2x+4): This is a multiplication of two binomials. We can use the distributive property (or FOIL method) to expand it:
- x(x^2 + 2x + 4) + 1(x^2 + 2x + 4)
- = x^3 + 2x^2 + 4x + x^2 + 2x + 4
- = x^3 + 3x^2 + 6x + 4
- -x^2(x+3): This is a multiplication of a monomial and a binomial. Again, use the distributive property:
- = -x^3 - 3x^2
Now, the equation looks like this:
x^3 + 3x^2 + 6x + 4 - x^3 - 3x^2 + 8 = 0
Step 2: Simplify the equation
Combine like terms to simplify the equation:
6x + 12 = 0
Step 3: Solve for x
Subtract 12 from both sides of the equation:
6x = -12
Divide both sides by 6:
x = -2
Solution:
The solution to the equation (x+1)(x^2+2x+4)-x^2(x+3)+8=0 is x = -2.