(x%5E2%2B8x%2B16)%3D6(x%2B4).jpeg "(x-1)(x^2+8x+16)=6(x+4)")
Solving the Equation: (x-1)(x^2+8x+16)=6(x+4)
In this article, we will solve the equation (x-1)(x^2+8x+16)=6(x+4) and find the values of x that satisfy the equation.
Expanding the Left-Hand Side
First, let's expand the left-hand side of the equation using the distributive property:
(x-1)(x^2+8x+16) = x^3 + 8x^2 + 16x - x^2 - 8x - 16
Combine like terms:
= x^3 + 7x^2 + 8x - 16
Expanding the Right-Hand Side
Now, let's expand the right-hand side of the equation:
6(x+4) = 6x + 24
Equating Both Sides
Now, equate both sides of the equation:
x^3 + 7x^2 + 8x - 16 = 6x + 24
Rearranging the Equation
Rearrange the equation to get all terms on one side:
x^3 + 7x^2 + 2x - 40 = 0
Factoring the Equation
Factor the equation:
(x - 4)(x^2 + 11x + 10) = 0
Solving for x
Now, solve for x:
x - 4 = 0 => x = 4
x^2 + 11x + 10 = 0
Solve the quadratic equation using the quadratic formula:
x = (-11 ± √(11^2 - 4(1)(10))) / 2(1)
x = (-11 ± √21) / 2
Therefore, the values of x that satisfy the equation (x-1)(x^2+8x+16)=6(x+4) are x = 4 and x = (-11 ± √21) / 2.
