Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find break even points
- Solve for x
- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
- Load more...
Find the break even points of the polynomial $\frac{x^2+5+x+6}{x+1}$ by putting it in the form of an equation and then set it equal to zero
Add the values $5$ and $6$
Multiply both sides of the equation by $x+1$
Any expression multiplied by $0$ is equal to $0$
To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=1$ and $c=11$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)
Multiply $-4$ times $11$
Multiply $-4$ times $11$
Subtract the values $1$ and $-44$
Subtract the values $1$ and $-44$
Calculate the power $\sqrt{-43}$ using complex numbers
Calculate the power $\sqrt{-43}$ using complex numbers
Multiply $-1$ times $6.5574385$
Combining all solutions, the $2$ solutions of the equation are
Verify that the solutions obtained are valid in the initial equation
The valid solutions to the equation are the ones that, when replaced in the original equation, don't make any denominator equal to $0$, since division by zero is not allowed